Relevant bibliographies by topics / KKT Conditions

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'KKT Conditions'

Author: Grafiati
Published: 4 June 2021
Last updated: 4 February 2022

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Journal articles on the topic "KKT Conditions"

1

Facchinei, Francisco, Christian Kanzow, and Simone Sagratella. "Solving quasi-variational inequalities via their KKT conditions." Mathematical Programming 144, no. 1-2 (February 12, 2013): 369–412. http://dx.doi.org/10.1007/s10107-013-0637-0.

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Nobakhtian, S., and M. R. Pouryayevali. "KKT Optimality Conditions and Nonsmooth Continuous Time Optimization Problems." Numerical Functional Analysis and Optimization 32, no. 11 (November 2011): 1175–89. http://dx.doi.org/10.1080/01630563.2011.592961.

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Ye, Jane J. "Constraint Qualifications and KKT Conditions for Bilevel Programming Problems." Mathematics of Operations Research 31, no. 4 (November 2006): 811–24. http://dx.doi.org/10.1287/moor.1060.0219.

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Rahman, Md Sadikur, Ali Akbar Shaikh, Irfan Ali, Asoke Kumar Bhunia, and Armin Fügenschuh. "A Theoretical Framework for Optimality Conditions of Nonlinear Type-2 Interval-Valued Unconstrained and Constrained Optimization Problems Using Type-2 Interval Order Relations." Mathematics 9, no. 8 (April 19, 2021): 908. http://dx.doi.org/10.3390/math9080908.

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In the traditional nonlinear optimization theory, the Karush-Kuhn-Tucker (KKT) optimality conditions for constrained optimization problems with inequality constraints play an essential role. The situation becomes challenging when the theory of traditional optimization is discussed under uncertainty. Several researchers have discussed the interval approach to tackle nonlinear optimization uncertainty and derived the optimality conditions. However, there are several realistic situations in which the interval approach is not suitable. This study aims to introduce the Type-2 interval approach to overcome the limitation of the classical interval approach. This study introduces Type-2 interval order relation and Type-2 interval-valued function concepts to derive generalized KKT optimality conditions for constrained optimization problems under uncertain environments. Then, the optimality conditions are discussed for the unconstrained Type-2 interval-valued optimization problem and after that, using these conditions, generalized KKT conditions are derived. Finally, the proposed approach is demonstrated by numerical examples.
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Gashaw, Amanu. "Solving Definite Quadratic Bi-Objective Programming Problems by KKT Conditions." Mathematical Modelling and Applications 2, no. 2 (2017): 21. http://dx.doi.org/10.11648/j.mma.20170202.12.

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Kien, Bui Trong, Nguyen Van Tuyen, and Jen-Chih Yao. "Second-Order KKT Optimality Conditions for MultiObjective Optimal Control Problems." SIAM Journal on Control and Optimization 56, no. 6 (January 2018): 4069–97. http://dx.doi.org/10.1137/17m1161750.

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Ho, Quyen. "Necessary and sufficient KKT optimality conditions in non-convex optimization." Optimization Letters 11, no. 1 (June 25, 2016): 41–46. http://dx.doi.org/10.1007/s11590-016-1054-0.

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Wu, Zili. "KKT conditions for weak ⁎ compact convex sets, theorems of the alternative, and optimality conditions." Journal of Functional Analysis 266, no. 2 (January 2014): 693–712. http://dx.doi.org/10.1016/j.jfa.2013.10.023.

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Dempe, Stephan, and Alain B. Zemkoho. "KKT Reformulation and Necessary Conditions for Optimality in Nonsmooth Bilevel Optimization." SIAM Journal on Optimization 24, no. 4 (January 2014): 1639–69. http://dx.doi.org/10.1137/130917715.

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Flores-Bazán, Fabián, and Giandomenico Mastroeni. "Characterizing FJ and KKT Conditions in Nonconvex Mathematical Programming with Applications." SIAM Journal on Optimization 25, no. 1 (January 2015): 647–76. http://dx.doi.org/10.1137/13094606x.

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Dissertations / Theses on the topic "KKT Conditions"

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Flor, Jose Alberto Ramos. "Tópicos em condições de otimalidade para otimização não linear." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-18102016-101943/.

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Esta tese é um estudo acerca da análise de convergência de vários métodos numéricos de primeira e de segunda ordem para resolver problemas de programação matemática e as condições de otimalidade associadas. Nossas principais ferramentas são as condições sequenciais de otimalidade. As condições sequenciais de otimalidade oferecem um quadro teórico para a análise de convergência para várias famílias de métodos de primeira ordem sob condições de qualificações fracas. Nesta tese, apresentamos, para cada condição sequencial de otimalidade, a condição de qualificação mínima associada e mostramos as relações com outras condições de qualificação conhecidas. Este fato tem implicações práticas, uma vez que enfraquece as hipóteses requeridas para a convergência de vários métodos numéricos cujos critérios de paradas estão associados às condições sequenciais de otimalidade. Ainda mais, esse tipo de resultado não pode ser melhorado usando outras condições de qualificações. Nós estendemos a noção de condições sequenciais de otimalidade de primeira ordem, para incorporar informações de segunda ordem. Apresentamos, segundo nosso conhecimento, a primeira condição sequencial de otimalidade de segunda ordem, adequada para a análise de convergência de vários métodos numéricos com convergência a pontos estacionários de segunda ordem, como por exemplo métodos baseados no Lagrangeano aumentado, regiões de confiança e SQP regularizado. Associada com a nova condição sequencial de segunda ordem, temos uma nova condição de qualificação, mais fraca que as outras condições de qualificações utilizadas para a análise de convergência para métodos numéricos de segunda ordem. Nós situamos essa nova condição de qualificação com respeito a outras condições de qualificação usadas em análise de convergência. Finalmente apresentamos outra razão pela qual a condição fraca necessária de segunda ordem é a condição de segunda ordem adequada quando lidarmos com a convergência de algoritmos práticos
This thesis deals with the convergence analysis for several rst-and-second-order numerical methods used to solve mathematical programming problems. Our main tools are the sequential optimality conditions. First-order sequential optimality conditions oer a framework to the study of the convergence analysis of several families of rst-order methods, under weak constraint qualications. In this thesis, we will introduce, for each sequential optimality condition the minimal constraint qualications associated with it and we will show their relationships with other constraint qualications. This fact has a practical aspect, since, we improve the convergence analysis of practical methods with stopping criteria associated with sequential optimality conditions. This results can not be improved by using another weak constraint qualications. We will extend the notion of rst-order sequential optimality conditions to incorporate secondorder information. We will introduce, to the best of our knowledge, the rst second-order sequential optimality condition, suitable to the study of the convergence analysis of several second-order methods including methods based on the augmented lagrangian, trust-region and regularized SQP. Associated with the second-order sequential optimality condition, we have a new constraint qualication weaker than all constraint qualications used for the convergence analysis of second-order methods. We show the relationships of this new constraint qualications with other constraint qualications used for algorithmic purposes. We will also present a new reason why the weak secondorder necessary condition is the natural second-order condition when we are dealing with practical numerical methods
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Sobral, Francisco Nogueira Calmon. "Programação em dois níveis: reformulação utilizando as condições KKT." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/45/45134/tde-11042008-163904/.

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Em um problema de natureza hierárquica, o nível mais influente toma certas decisões que afetam o comportamento dos níveis inferiores. Cada decisão do nível mais influente é considerada como fixa pelos níveis inferiores, que, com tais informações, tomam decisões que maximizam seus objetivos. Essas decisões podem influenciar os resultados obtidos pelo nível superior, que, por sua vez, também anseia pela decisão ótima. Em programação matemática, este problema é modelado como um problema de programação em níveis. Neste trabalho, consideramos uma classe particular de problemas de programação em níveis: os problemas de programação matemática em dois níveis. Estudamos uma técnica de resolução que consiste em substituir o problema do nível inferior por suas condições necessárias de primeira ordem, que podem ser formuladas de diversas maneiras, conforme as restrições de complementaridade são modificadas. O novo problema torna-se um problema de programação não linear e pode ser resolvido com algoritmos clássicos de otimização. Com o auxílio de condições de otimalidade de primeira e segunda ordem mostramos as relações entre o problema original e o problema reformulado. Aplicamos a técnica a problemas encontrados na literatura, analisamos o seu comportamento e apresentamos estratégias para eliminar certos inconvenientes encontrados.
In problems of hierarchical nature, the choices made by the most influential level - the so-called leader - affect the behavior of the lower levels. For each one of the leader\'s decisions there is a response from the lower levels, which maximizes the value of their respective objectives. These optimal choices, in return, may have influence in the results achieved by the leader, which also wants to make the optimal choices. In mathematical programming, this kind of problem is described as a multilevel programming problem. The present work considers a specific kind of multilevel problem: the bilevel mathematical problem. We study a resolution technique which consists in replacing the lower level problem by its necessary first order conditions, which can be formulated in various ways, as complementarity constraints occur and are modified. The new reformulated problem is a nonlinear programming problem which can be solved by classical optimization methods. Using first and second order optimality conditions, we show the relations between the original bilevel problem and the reformulated problem. We apply the described technique to solve a set of bilevel problems taken from the literature, analyse their behavior and discuss strategies to prevent undesirable difficulties that may arise.
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Sousa, Vanusa Alves de. "A função barreira logarítmica associada ao método de Newton modificado para a resolução do problema de fluxo de potência ótimo." Universidade de São Paulo, 2001. http://www.teses.usp.br/teses/disponiveis/18/18133/tde-18042016-111117/.

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Este trabalho descreve uma abordagem do método primal-dual barreira logarítmica (MPDBL) associado ao método de Newton modificado para a resolução do problema de fluxo barreira logarítmica e nas condições de primeira ordem de Karush-Kuhn-Tucker (KKT). O sistema de equações resultantes das condições de estacionaridade, da função Lagrangiana, foi resolvido pelo método de Newton modificado. Na implementação computacional foram usadas as técnicas de esparsidade. Os resultados numéricos dos testes realizados em 5 sistemas (3, 14, 30, 57 e 118 barras) evidenciam o potencial desta metodologia na solução do problema de FPO.
This work describes an approach on primal-dual logarithmic barrier for solving the optimal power flow problem (OPF). The investigation was based on the logarithmic barrier function and Karush-Kuhn-Tucker (KKT) first-order necessary conditions. The equation system, obtained from the stationary conditions of the Lagrangian function, was solved using the Newton\'s modified method. The implementation was performed using sparsity techniques. The numerical results, carried out in five systems (3, 14,30, 57 and 118 bus), demonstrate the reliability of this approach in the solution OPF problem.
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Pereira, Leandro Sereno. "Despacho ativo com restrição na transmissão via método de barreira logarítmica." Universidade de São Paulo, 2002. http://www.teses.usp.br/teses/disponiveis/18/18133/tde-02062017-104334/.

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Este trabalho apresenta uma abordagem do método da função barreira logarítmica (MFBL) para a resolução do problema de fluxo de potência ótimo (FPO). A pesquisa fundamenta-se metodologicamente na função barreira logarítmica e nas condições de primeira ordem de Karush-Kuhn-Tucker (KKT). Para a solução do sistema de equações resultantes das condições de estacionaridade, da função Lagrangiana, utiliza-se o método de Newton. Na implementação computacional utiliza-se técnicas de esparsidade. Através dos resultados numéricos dos testes realizados em 5 sistemas (3, 8, 14, 30 e 118 barras) evidencia-se o potencial desta metodologia na solução do problema de FPO.
This work describes an approach on logarithmic barrier function method to solving the optimal power flow (OPF) problem. Search was based on the logarithmic barrier function and first order conditions of Karush-Kuhn-Tucker (KKT). To solve the equation system, obtained from the stationary conditions of the Lagrangian function, is used the Newton method. Implementation is performed using sparsity techniques. The numerical results, carried out in five systems (3, 8, 14, 30 and 118 bus), demonstrate the reliability of this approach in the solution OPF problem.
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Mehlitz, Patrick. "Optimierung in normierten Räumen." Thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2013. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-119320.

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Die Arbeit abstrahiert bekannte Konzepte der endlichdimensionalen Optimierung im Hinblick auf deren Anwendung in Banachräumen. Hierfür werden zunächst grundlegende Elemente der Funktionalanalysis wie schwache Konvergenz, Dualräume und Reflexivität vorgestellt. Anschließend erfolgt eine kurze Einführung in die Thematik der Fréchet-Differenzierbarkeit und eine Abstraktion des Begriffs der partiellen Ordnungsrelation in normierten Räumen. Nach der Formulierung eines allgemeinen Existenzsatzes für globale Optimallösungen von abstrakten Optimierungsaufgaben werden notwendige Optimalitätsbedingungen vom Karush-Kuhn-Tucker-Typ hergeleitet. Abschließend wird eine hinreichende Optimalitätsbedingung vom Karush-Kuhn-Tucker-Typ unter verallgemeinerten Konvexitätsvoraussetzungen verifiziert.
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Lerotholi, Sekhonyana. "The role of salinity as an abiotic driver of ecological condition in a rural agricultural catchment." Thesis, Rhodes University, 2006. http://hdl.handle.net/10962/d1005528.

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The Kat River is an agricultural catchment that drains salt rich geology. Potential salinity impacts on ecological condition of the river were investigated. Monthly salt concentrations and flow discharges were monitored at ten sites along the Kat River below the Kat Dam. Monthly salt loads were computed to relate salinity to land use and ionic data used to assess the toxicity of major salts using the TIMS model. Concentration duration curves for sodium chloride were derived from flow concentration relationships, representing sodium chloride concentrations to which the aquatic ecosystem had been exposed. The ecological condition was assessed at nineteen sites using SASS5 biotic index over four seasons. Finally, the modelled instream salt concentrations and bioasessments were evaluated in terms of the modelled level of species protection afforded at different salt concentrations. Species Sensitivity Distributions (SSDs) were used for this exercise. There was a general downstream increase in salinity with the minimum concentrations recorded at the Fairbain tributary (84 mg/L) and maximum levels at the sewage outfall in Fort Beaufort (1222 mg/L). There was evidence that citrus irrigation upstream of Fort Beaufort increased salinisation. Sodium chloride, and to a lesser extent magnesium sulphate, were the dominant salts in the Kat River catchment, with the latter being more toxic. However these had little or no impact on the aquatic ecosystem. Flow-derived sodium chloride concentrations showed that both the Balfour and Blinkwater tributaries were in a fair/ poor condition. However with regard to ecological condition, it was demonstrated that the river is generally in a good state except for the Blinkwater River and the lower catchment. Degraded habitat condition at the Blinkwater was responsible for poor ecological condition. Integrating SSD derived classes, sodium chloride classes and ecological condition indicated that sodium chloride is a driver of ecological condition at the sewage treatment works and the subsequent site (only two of nineteen biomonitoring sites).
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Jackson, Remonica, Stacy D. Brown, and Paul Lewis. "Comparative Stability of Compounded Omeprazole Suspension Versus Commercial Omeprazole Kit When Stored in Oral Syringes Under Refrigerated Conditions." Digital Commons @ East Tennessee State University, 2019. https://dc.etsu.edu/etsu-works/7847.

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Purpose:Omeprazole is a proton pump inhibitor (PPI) used in the treatment of gastrointestinal conditions, such as gastrointestinal esophageal reflux disease (GERD). Omeprazole is often prepared as an oral suspension to accommodate certain patients. Historically, oral suspensions of omeprazole were prepared using pharmaceutical compounding with sodium bicarbonate, but a kit for preparation of omeprazole oral suspension is available, FIRST® - Omeprazole. The purpose of this project is to compare the stability of the active pharmaceutical ingredient (API), omeprazole, in the FIRST® kit product to a traditionally compounded omeprazole suspension, when stored in refrigerated unit-dosed syringes. Methods: Five 100-mL batches of compounded omeprazole oral suspension (2 mg/mL) and five 300-mL kits of FIRST® - Omeprazole were prepared by a licensed pharmacist, and aliquoted into 5-mL doses in clear luer-lock plastic oral syringes, and stored at refrigerated temperature (2-8oC). Omeprazole concentration was assessed in each batch/kit on the day of preparation. Triplicate syringes from each batch/kit (n = 15 per test group per day) were removed after 7 days, 14 days, 21 days, and 30 days of refrigerated storage. Samples were diluted to assay concentration (1 mg/mL) in ion-free water and filtered using a 0.22-micron microcentrifuge filter tube. Samples were analyzed for omeprazole recovery using a validated high-performance liquid chromatography with ultraviolet detection (HPLC-UV) method. Recovery was quantitatively assessed by comparing sample peak area to a freshly prepared calibration curve (1 – 0.125 mg/mL) using United States Pharmacopoeia (USP) reference standard on each day of sampling. Refrigerator temperatures were recorded daily using a digital thermometer. Results:Stability was defined as recovery of 90 - 110% of initial concentration of API. For the FIRST® - Omeprazole samples, the chemical potency remained within this window for the entire study period of 30 days. The compounded omeprazole suspension demonstrated a less than 90% average recovery at the day 21 sample. Furthermore, a statistically significant difference in the initial concentration was detected on the day of compounding (p = 0.0244), with the compounded omeprazole starting at 1.89 ± 0.10 mg/mL and the FIRST® - Omeprazole at 1.98 ± 0.04 mg/mL. After 30 days, the compounded omeprazole suspension had an 89.13% average API recovery (standard deviation; ± 5.17%) and the FIRST® - Omeprazole 97.20% API recovery (± 3.59%). Conclusion:Both traditionally compounded omeprazole suspension (2mg/mL) and FIRST® - Omeprazole suspension (2mg/mL) may be stored in clear luer-lock oral syringes under refrigeration for 14 days, and retain potency between 90 to 110% based on initial concentration. Furthermore, the FIRST® - Omeprazole suspension can be stored for the duration of the product’s beyond-use date of 30 days and retain potency between 90 to 110% of initial concentration or label claim. Finally, the data suggest that API concentration in FIRST® - Omeprazole suspension is more consistent from batch to batch than traditionally compounded omeprazole suspension.
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Pruchnicka, Joanna. "A BETTER WAY TO LIVE WITH A CHRONIC CONDITION : Envisioning transition kit for women living with endometriosis." Thesis, Umeå universitet, Designhögskolan vid Umeå universitet, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-149537.

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This project explores the question of how to support women living with endometriosis in the transition into live with a chronic condition while maintaining the best possible quality of life. Design process was planned out and exercises in four steps - preparations and background research (outlining well-being perspective, desk research, research online via social media), design research (multiple surveys, interviews, reflections online, co-creation sessions, probing, interviews following probing with co-creation sessions, ideation sessions, analysis), explorations (creation of directions, analysis, initial concepts creation, feedback, synthesis, design proposal, feedback and evaluation sessions, design improvements) and final design proposal. Activities were aiming to repeatedly open up the scope of the project and then through the analysis of each phase narrow it down again following diamond shape. One important aspect of the process was to engage women living with endometriosis as well as their loved ones throughout the whole process and design together instead of designing for them. Of course, experts were consulted as well to make sure project is following standards of medical care, but the primary focus on the users was important since the product was shaped rather as a lifestyle change facilitator as well as data collection tool rather than a strictly medical solution. The outcome of the project is a flexible system VEA serving as a transition kit for women diagnosed with endometriosis, but also early detection screening tool and awareness platform for those who haven’t been diagnosed yet. Even though this might seem complicated I’ll try to explain why only this kind of a multifaceted approach can fully support women in their journey toward their best possible quality of life. VEA allows users to access Habit Nooks supporting them in introducing changes while guided by experts and supported by the community. Physical tracker allowing to track symptoms together with the Data Dashboard allow users to explore data patterns and make informed decisions. The system gives also an opportunity to get in touch with experts via calls or structured long-term programs. Beside the design proposal project was closed with a series of reflection touching on the bias in a medical field and how it might affect healthcare design, as well as designer’s experience of working on a project with a personal relevance.
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Herrich, Markus. "Local Convergence of Newton-type Methods for Nonsmooth Constrained Equations and Applications." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-159569.

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In this thesis we consider constrained systems of equations. The focus is on local Newton-type methods for the solution of constrained systems which converge locally quadratically under mild assumptions implying neither local uniqueness of solutions nor differentiability of the equation function at solutions. The first aim of this thesis is to improve existing local convergence results of the constrained Levenberg-Marquardt method. To this end, we describe a general Newton-type algorithm. Then we prove local quadratic convergence of this general algorithm under the same four assumptions which were recently used for the local convergence analysis of the LP-Newton method. Afterwards, we show that, besides the LP-Newton method, the constrained Levenberg-Marquardt method can be regarded as a special realization of the general Newton-type algorithm and therefore enjoys the same local convergence properties. Thus, local quadratic convergence of a nonsmooth constrained Levenberg-Marquardt method is proved without requiring conditions implying the local uniqueness of solutions. As already mentioned, we use four assumptions for the local convergence analysis of the general Newton-type algorithm. The second aim of this thesis is a detailed discussion of these convergence assumptions for the case that the equation function of the constrained system is piecewise continuously differentiable. Some of the convergence assumptions seem quite technical and difficult to check. Therefore, we look for sufficient conditions which are still mild but which seem to be more familiar. We will particularly prove that the whole set of the convergence assumptions holds if some set of local error bound conditions is satisfied and in addition the feasible set of the constrained system excludes those zeros of the selection functions which are not zeros of the equation function itself, at least in a sufficiently small neighborhood of some fixed solution. We apply our results to constrained systems arising from complementarity systems, i.e., systems of equations and inequalities which contain complementarity constraints. Our new conditions are discussed for a suitable reformulation of the complementarity system as constrained system of equations by means of the minimum function. In particular, it will turn out that the whole set of the convergence assumptions is actually implied by some set of local error bound conditions. In addition, we provide a new constant rank condition implying the whole set of the convergence assumptions. Particularly, we provide adapted formulations of our new conditions for special classes of complementarity systems. We consider Karush-Kuhn-Tucker (KKT) systems arising from optimization problems, variational inequalities, or generalized Nash equilibrium problems (GNEPs) and Fritz-John (FJ) systems arising from GNEPs. Thus, we obtain for each problem class conditions which guarantee local quadratic convergence of the general Newton-type algorithm and its special realizations to a solution of the particular problem. Moreover, we prove for FJ systems of GNEPs that generically some full row rank condition is satisfied at any solution of the FJ system of a GNEP. The latter condition implies the whole set of the convergence assumptions if the functions which characterize the GNEP are sufficiently smooth. Finally, we describe an idea for a possible globalization of our Newton-type methods, at least for the case that the constrained system arises from a certain smooth reformulation of the KKT system of a GNEP. More precisely, a hybrid method is presented whose local part is the LP-Newton method. The hybrid method turns out to be, under appropriate conditions, both globally and locally quadratically convergent.
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De, Wet C. J., Phumeza Lujabe, and Nosipho Metele. "Resettlement in the Border/Ciskei region of South Africa." Rhodes University, Institute of Social and Economic Research, 1996. http://hdl.handle.net/10962/2849.

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This paper presents the findings of part of a research project entitled "Population Mobility and Settlement Patterns in the Eastern Cape, 1950 to 1990", which was funded by the Human Sciences Research Council. The part of the project with which this paper is concerned, is the study of resettlement in the Border/Ciskei area of the (new) Eastern Cape Province. It involves two main foci: a) the Whittlesea district of the former Ciskei, where research was done in the resettlement area of Sada (where findings are compared with research done there in 1981) and Dongwe; and b) the Fort Beaufort area, where we looked at the two 'black spot' communities of Upisdraai and Gqugesi which were uprooted and moved to the Fort Beaufort township of Bhofolo in the 1960s, and at the establishment of black citrus farmers in the Kat River Valley in the late 1980s, on previously White owned farms which were bought out by the (then) Ciskei government. In the Conclusion, some important differences are suggested between resettlement in the Eastern Cape and in QwaQwa, one of the areas of South Africa that has been most severely affected by resettlement. Ways in which the South African material may be seen in terms of prevailing models for the analysis of resettlement, and may provide an input for the modification of these approaches, are briefly considered.
Digitised by Rhodes University Library on behalf of the Institute of Social and Economic Research (ISER)
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Books on the topic "KKT Conditions"

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Csath, Magdolna. Kit válasszunk?: Választási iránytű. Budapest: Kairosz, 2010.

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Tokareva, Zinaida Ivanovna. Respublika Kot-d'Ivuar: Spravochnik. Moskva: "Nauka," Glav. red. vostochnoĭ lit-ry, 1990.

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Riggs, Maribeth. The women's home remedy kit: Simple recipes for treating common health conditions. New York: Pocket Books, 1995.

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Uri ttang kot kot apʻŭji anŭn kot i ŏmne: Yi Kyŏng-jae kyosu ŭi hwanʾgyŏng kihaeng. Sŏul-si: Pʻurŭn San, 1994.

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Pānʻīam, Watchara. Pāk kat tīn mai thīp. Krung Thēp Mahā Nakhō̜n: Samnakphim Matichon, 2003.

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Chʻotpul, ŏttŏkʻe pol kot inʼga. Sŏul-si: Ullyŏk, 2009.

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Sogŭm kkot namu. Sŏul: Humanitʻasŭ, 2007.

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Gender resource kit supplementary reading material. Gaborone, Botswana: Gender Unit, SADC Secretariat, 2003.

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1960-, Yun Tong-gu, ed. Pyŏrang kkŭt e sŏn Pukhan. Sŏul-si: Hanŏl Midiŏ, 2009.

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1960-, Yun Tong-gu, ed. Pyŏrang kkŭt e sŏn Pukhan. Sŏul-si: Hanŏl Midiŏ, 2009.

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Book chapters on the topic "KKT Conditions"

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Gass, Saul I., and Carl M. Harris. "KKT conditions." In Encyclopedia of Operations Research and Management Science, 431. New York, NY: Springer US, 2001. http://dx.doi.org/10.1007/1-4020-0611-x_498.

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Dutta, Joydeep. "Strong KKT, Second Order Conditions and Non-solid Cones in Vector Optimization." In Vector Optimization, 127–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21114-0_5.

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Yang, P. C., H. M. Wee, S. L. Chung, and S. H. Kang. "Constrained Optimization of a Newsboy Problem with Return Policy Using KKT Conditions and GA." In New Trends in Applied Artificial Intelligence, 227–37. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-73325-6_23.

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Cartis, Coralia, Nicholas I. M. Gould, and Philippe L. Toint. "Evaluation Complexity Bounds for Smooth Constrained Nonlinear Optimization Using Scaled KKT Conditions and High-Order Models." In Approximation and Optimization, 5–26. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-12767-1_2.

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Gass, Saul I., and Carl M. Harris. "Kuhn-tucker (Kt) conditions." In Encyclopedia of Operations Research and Management Science, 435–36. New York, NY: Springer US, 2001. http://dx.doi.org/10.1007/1-4020-0611-x_508.

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"KKT Conditions." In Encyclopedia of Operations Research and Management Science, 834. Boston, MA: Springer US, 2013. http://dx.doi.org/10.1007/978-1-4419-1153-7_200362.

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"Karush-Kuhn-Tucker (KKT) Conditions." In Encyclopedia of Operations Research and Management Science, 833–34. Boston, MA: Springer US, 2013. http://dx.doi.org/10.1007/978-1-4419-1153-7_200359.

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"Chapter 11: The KKT Conditions." In Introduction to Nonlinear Optimization, 207–35. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2014. http://dx.doi.org/10.1137/1.9781611973655.ch11.

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"Appendix G: KKT optimality conditions." In Modelling Distributed Energy Resources in Energy Service Networks, 185. Institution of Engineering and Technology, 2013. http://dx.doi.org/10.1049/pbrn016e_appendixg.

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"Representation of the Feasible Set and KKT Conditions." In Optimality Conditions in Convex Optimization, 333–44. CRC Press, 2011. http://dx.doi.org/10.1201/b11156-14.

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Conference papers on the topic "KKT Conditions"

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Wu, Chongming, Xiaodan Wang, Dongying Bai, and Hongda Zhang. "Fast Incremental Learning Algorithm of SVM on KKT Conditions." In 2009 Sixth International Conference on Fuzzy Systems and Knowledge Discovery. IEEE, 2009. http://dx.doi.org/10.1109/fskd.2009.784.

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Adegbege, Ambrose A., and William P. Heath. "Multivariable algebraic loops with complementarity constraints enforcing some KKT conditions." In 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2014. http://dx.doi.org/10.1109/allerton.2014.7028568.

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Zhang, Jianke. "Optimality conditions for multiobjective programming problems with G-KKT-pseudoinvexity." In 2013 9th International Conference on Natural Computation (ICNC). IEEE, 2013. http://dx.doi.org/10.1109/icnc.2013.6818050.

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Tulshyan, Rupesh, Ramnik Arora, Kalyanmoy Deb, and Joydeep Dutta. "Investigating EA solutions for approximate KKT conditions in smooth problems." In the 12th annual conference. New York, New York, USA: ACM Press, 2010. http://dx.doi.org/10.1145/1830483.1830609.

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Yu, Xin, Bingchang Wang, and Hailing Dong. "A distributed algorithm based on KKT conditions for convex intersection computation." In 2017 Chinese Automation Congress (CAC). IEEE, 2017. http://dx.doi.org/10.1109/cac.2017.8244167.

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Kim, Hyun Jun, Ye Seul Son, and Joon Tae Kim. "KKT-conditions based resource allocation algorithm for DASH streaming service over LTE." In 2018 IEEE International Conference on Consumer Electronics (ICCE). IEEE, 2018. http://dx.doi.org/10.1109/icce.2018.8326221.

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Xu, Meng, Georges Fadel, and Margaret M. Wiecek. "Dual Residual for Distributed Augmented Lagrangian Coordination Based on Optimality Conditions." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47002.

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Augmented Lagrangian Coordination (ALC) is one of the more popular coordination strategies for decomposition based optimization. It employs the augmented Lagrangian relaxation approach and has shown great improvements in terms of efficiency and solution accuracy when compared to other methods addressing the same type of problem. Additionally, by offering two variants: the centralized ALC in which an artificial master problem in the upper level is created to coordinate all the sub-problems in the lower level, and the distributed ALC in which coordination can be performed directly between sub-problems without a master problem, ALC provides more flexibility than other methods. However, the initial setting and the update strategy of the penalty weights in ALC still significantly affect its performance and thus are worth further research. For centralized ALC, the non-monotone weight update strategy based on the theory of dual residual has shown very good improvements over the traditional monotone update, in which the penalty weights can either increase or decrease. In this paper, we extend the research on the dual residual in centralized ALC to the distributed ALC. Through applying the Karush-Kuhn-Tucker (KKT) optimality conditions to the All-In-One (AIO) and decomposed problems, the necessary conditions for the decomposed solution to be optimal are derived, which leads to the definition of primal and dual residuals in distributed ALC. A new non-monotone weight based on both residuals is then proposed, by which all AIO KKT conditions are guaranteed after decomposition. Numerical tests are conducted on two mathematical problems and one engineering problem and the performances of the new update are compared to those of the traditional update. The results show that our proposed methods improve the process efficiency, accuracy, and robustness for distributed ALC.
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Kanakasabai, Pugazhendhi, and Anoop K. Dhingra. "An Approach for Uni-Level Reliability Based Design Optimization Using Cross-Entropy Method." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70691.

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In this paper a novel approach is proposed to solve the reliability based design optimization (RBDO) problem, which is translated into a single-level problem using Karush-Kuhn-Tucker (KKT) conditions. The transformation of a bi-level RBDO problem into a single-level problem using KKT conditions introduces several equality constraints in the single-level problem definition. Presence of multiple equality constraints poses numerical difficulty to the gradient based optimizers, hence a robust algorithm to solve the single-level RBDO problem is proposed in this paper using an alternative approach. The proposed approach uses an exterior penalty based cross-entropy (CE) method to solve the uni-level RBDO problem. This approach is shown to be robust in handling equality constraints. The three example problems solved in this paper also shows that the algorithm works well with different starting points used for the design variables.
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Dong, Jiawei, and Won-jong Kim. "Bandwidth Allocation of Networked Control Systems With Exponential Approximation." In ASME 2013 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/dscc2013-3778.

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This paper investigates bandwidth allocation of networked control systems (NCSs) with nonlinear-programming techniques. The bandwidth utilization (BU) is defined in terms of sampling frequency. An exponential approximation is formulated to describe system performance versus the sampling frequencies. The optimal sampling frequencies are obtained by solving the approximation with Karush-Kuhn-Tucker (KKT) conditions. Simulation and experimental results verify the effectiveness of the proposed approximation. The exponential approximation can minimize the BU so that the plants can be scheduled along with the system PIFs being optimized.
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Case, Sarah S., and Kate S. Whitefoot. "Global Product Design Platforming: A Comparison of Two Methods to Find Equilibrium Solutions." In ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/detc2020-22658.

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Abstract We examine optimal-profit product design platforming problems for products sold across multiple markets. Firms have an incentive to platform to take advantage of cost reductions that are possible with increased production quantity, such as learning-by-doing. However, platforming may decrease sales compared to if the designs were customized for each market. The problem can be represented as a Nash equilibrium between multiple competing firms, each with a nonconvex mixed-integer nonlinear programing (MINLP) problem for maximizing their individual profits. We derive the Karush-Kuhn-Tucker (KKT) conditions for the problem and compare results from two algorithmic approaches: (1) an iterative MINLP approach that uses the BARON algorithm to solve each firm’s design and platforming problem and iterates until convergence to an equilibrium, and (2) an approach that solves the KKT conditions directly holding platforming decisions fixed, and compares profits for these platforming decisions to find an equilibrium. Results are presented for a case study of plug-in hybrid electric vehicles (PHEVs) where firms choose whether or not to platform the battery pack across the U.S. and China, and set the optimal battery capacity. We vary the learning rate and the difference in consumer willingness to pay for all-electric range between China and the U.S. Both algorithms agree on the same equilibrium solution in 98.4% of the cases. Results show that the optimum for each firm is to platform when learning rates are low, or the difference between optimal battery capacity in each market is relatively small.
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