Relevant bibliographies by topics / Convex duality theory

Contents

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

Academic literature on the topic 'Convex duality theory'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Convex duality theory"

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Shapiro, Alexander. "On duality theory of convex semi-infinite programming." Optimization 54, no. 6 (December 2005): 535–43. http://dx.doi.org/10.1080/02331930500342823.

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Sun, Wenyu, Chengjin Li, and Raimundo J. B. Sampaio. "On duality theory for non-convex semidefinite programming." Annals of Operations Research 186, no. 1 (March 23, 2011): 331–43. http://dx.doi.org/10.1007/s10479-011-0861-z.

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Richardt, J., F. Karl, and C. Müller. "Connections between fuzzy theory, simulated annealing, and convex duality." Fuzzy Sets and Systems 96, no. 3 (June 1998): 307–34. http://dx.doi.org/10.1016/s0165-0114(96)00301-6.

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Brinkhuis, Ya, and V. M. Tikhomirov. "Duality and calculus of convex objects (theory and applications)." Sbornik: Mathematics 198, no. 2 (February 28, 2007): 171–206. http://dx.doi.org/10.1070/sm2007v198n02abeh003833.

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Lee, Mi Jin, Jong Yeoul Park, and Young Chel Kwon. "Duality in the optimal control for damped hyperbolic systems with positive control." International Journal of Mathematics and Mathematical Sciences 2003, no. 27 (2003): 1703–14. http://dx.doi.org/10.1155/s0161171203209273.

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We study the duality theory for damped hyperbolic equations. These systems have positive controls and convex cost functionals. Our main results lie in the application of duality theorem, that is,inf J=sup K, on various cost functions.
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Ekeland, Ivar. "A duality theory for some non-convex functions of matrices." Ricerche di Matematica 55, no. 1 (July 2006): 1–12. http://dx.doi.org/10.1007/s11587-006-0001-2.

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Park, Jong Yeoul, and Mi Jin Lee. "Duality in the optimal control of hyperbolic equations with positive controls." International Journal of Mathematics and Mathematical Sciences 23, no. 3 (2000): 181–88. http://dx.doi.org/10.1155/s0161171200002015.

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Lan, K. Q., and J. R. L. Webb. "A-properness and fixed point theorems for dissipative type maps." Abstract and Applied Analysis 4, no. 2 (1999): 83–100. http://dx.doi.org/10.1155/s108533759900010x.

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We obtain newA-properness results for demicontinuous, dissipative type mappings defined only on closed convex subsets of a Banach spaceXwith uniformly convex dual and which satisfy a property called weakly inward. The method relies on a new property of the duality mapping in such spaces. New fixed point results are obtained by utilising a theory of fixed point index.
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CHAN, W. L., and S. P. YUNG. "Duality Theory for the Linear-Convex Optimal Control Problem with Delays." IMA Journal of Mathematical Control and Information 4, no. 3 (1987): 251–62. http://dx.doi.org/10.1093/imamci/4.3.251.

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Auslender, A., R. Cominetti, and J. P. Crouziex. "Convex Functions with Unbounded Level Sets and Applications to Duality Theory." SIAM Journal on Optimization 3, no. 4 (November 1993): 669–87. http://dx.doi.org/10.1137/0803034.

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Dissertations / Theses on the topic "Convex duality theory"

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Vargyas, Emese Tünde. "Duality for convex composed programming problems." Doctoral thesis, Universitätsbibliothek Chemnitz, 2004. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200401793.

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The goal of this work is to present a conjugate duality treatment of composed programming as well as to give an overview of some recent developments in both scalar and multiobjective optimization. In order to do this, first we study a single-objective optimization problem, in which the objective function as well as the constraints are given by composed functions. By means of the conjugacy approach based on the perturbation theory, we provide different kinds of dual problems to it and examine the relations between the optimal objective values of the duals. Given some additional assumptions, we verify the equality between the optimal objective values of the duals and strong duality between the primal and the dual problems, respectively. Having proved the strong duality, we derive the optimality conditions for each of these duals. As special cases of the original problem, we study the duality for the classical optimization problem with inequality constraints and the optimization problem without constraints. The second part of this work is devoted to location analysis. Considering first the location model with monotonic gauges, it turns out that the same conjugate duality principle can be used also for solving this kind of problems. Taking in the objective function instead of the monotonic gauges several norms, investigations concerning duality for different location problems are made. We finish our investigations with the study of composed multiobjective optimization problems. In doing like this, first we scalarize this problem and study the scalarized one by using the conjugacy approach developed before. The optimality conditions which we obtain in this case allow us to construct a multiobjective dual problem to the primal one. Additionally the weak and strong duality are proved. In conclusion, some special cases of the composed multiobjective optimization problem are considered. Once the general problem has been treated, particularizing the results, we construct a multiobjective dual for each of them and verify the weak and strong dualities
In dieser Arbeit wird, anhand der sogenannten konjugierten Dualitätstheorie, ein allgemeines Dualitätsverfahren für die Untersuchung verschiedener Optimierungsaufgaben dargestellt. Um dieses Ziel zu erreichen wird zuerst eine allgemeine Optimierungsaufgabe betrachtet, wobei sowohl die Zielfunktion als auch die Nebenbedingungen zusammengesetzte Funktionen sind. Mit Hilfe der konjugierten Dualitätstheorie, die auf der sogenannten Störungstheorie basiert, werden für die primale Aufgabe drei verschiedene duale Aufgaben konstruiert und weiterhin die Beziehungen zwischen deren optimalen Zielfunktionswerten untersucht. Unter geeigneten Konvexitäts- und Monotonievoraussetzungen wird die Gleichheit dieser optimalen Zielfunktionswerte und zusätzlich die Existenz der starken Dualität zwischen der primalen und den entsprechenden dualen Aufgaben bewiesen. In Zusammenhang mit der starken Dualität werden Optimalitätsbedingungen hergeleitet. Die Ergebnisse werden abgerundet durch die Betrachtung zweier Spezialfälle, nämlich die klassische restringierte bzw. unrestringierte Optimierungsaufgabe, für welche sich die aus der Literatur bekannten Dualitätsergebnisse ergeben. Der zweite Teil der Arbeit ist der Dualität bei Standortproblemen gewidmet. Dazu wird ein sehr allgemeines Standortproblem mit konvexer zusammengesetzter Zielfunktion in Form eines Gauges formuliert, für das die entsprechenden Dualitätsaussagen abgeleitet werden. Als Spezialfälle werden Optimierungsaufgaben mit monotonen Normen betrachtet. Insbesondere lassen sich Dualitätsaussagen und Optimalitätsbedingungen für das klassische Weber und Minmax Standortproblem mit Gauges als Zielfunktion herleiten. Das letzte Kapitel verallgemeinert die Dualitätsaussagen, die im zweiten Kapitel erhalten wurden, auf multikriterielle Optimierungsprobleme. Mit Hilfe geeigneter Skalarisierungen betrachten wir zuerst ein zu der multikriteriellen Optimierungsaufgabe zugeordnetes skalares Problem. Anhand der in diesem Fall erhaltenen Optimalitätsbedingungen formulieren wir das multikriterielle Dualproblem. Weiterhin beweisen wir die schwache und, unter bestimmten Annahmen, die starke Dualität. Durch Spezialisierung der Zielfunktionen bzw. Nebenbedingungen resultieren die klassischen konvexen Mehrzielprobleme mit Ungleichungs- und Mengenrestriktionen. Als weitere Anwendungen werden vektorielle Standortprobleme betrachtet, zu denen wir entsprechende duale Aufgaben formulieren
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Lorenz, Nicole. "Application of the Duality Theory." Doctoral thesis, Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-94108.

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The aim of this thesis is to present new results concerning duality in scalar optimization. We show how the theory can be applied to optimization problems arising in the theory of risk measures, portfolio optimization and machine learning. First we give some notations and preliminaries we need within the thesis. After that we recall how the well-known Lagrange dual problem can be derived by using the general perturbation theory and give some generalized interior point regularity conditions used in the literature. Using these facts we consider some special scalar optimization problems having a composed objective function and geometric (and cone) constraints. We derive their duals, give strong duality results and optimality condition using some regularity conditions. Thus we complete and/or extend some results in the literature especially by using the mentioned regularity conditions, which are weaker than the classical ones. We further consider a scalar optimization problem having single chance constraints and a convex objective function. We also derive its dual, give a strong duality result and further consider a special case of this problem. Thus we show how the conjugate duality theory can be used for stochastic programming problems and extend some results given in the literature. In the third chapter of this thesis we consider convex risk and deviation measures. We present some more general measures than the ones given in the literature and derive formulas for their conjugate functions. Using these we calculate some dual representation formulas for the risk and deviation measures and correct some formulas in the literature. Finally we proof some subdifferential formulas for measures and risk functions by using the facts above. The generalized deviation measures we introduced in the previous chapter can be used to formulate some portfolio optimization problems we consider in the fourth chapter. Their duals, strong duality results and optimality conditions are derived by using the general theory and the conjugate functions, respectively, given in the second and third chapter. Analogous calculations are done for a portfolio optimization problem having single chance constraints using the general theory given in the second chapter. Thus we give an application of the duality theory in the well-developed field of portfolio optimization. We close this thesis by considering a general Support Vector Machines problem and derive its dual using the conjugate duality theory. We give a strong duality result and necessary as well as sufficient optimality conditions. By considering different cost functions we get problems for Support Vector Regression and Support Vector Classification. We extend the results given in the literature by dropping the assumption of invertibility of the kernel matrix. We use a cost function that generalizes the well-known Vapnik's ε-insensitive loss and consider the optimization problems that arise by using this. We show how the general theory can be applied for a real data set, especially we predict the concrete compressive strength by using a special Support Vector Regression problem.
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White, Edward C. Jr. "Polar - legendre duality in convex geometry and geometric flows." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24689.

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Hare, David Edwin George. "A duality theory for Banach spaces with the Convex Point-of-Continuity Property." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/27313.

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A norm ||⋅|| on a Banach space X is Fréchet differentiable at x ∈ X if there is a functional ∫∈ X* such that [Formula Omitted] This concept reflects the smoothness characteristics of X. A dual Banach space X* has the Radon-Nikodym Property (RNP) if whenever C ⊂ X* is weak*-compact and convex, and ∈ > 0, there is an x ∈ X and an ⍺ > 0 such that diameter [Formula Omitted] this property reflects the convexity characteristics of X*. Culminating several years of work by many researchers, the following theorem established a strong connection between the smoothness of X and the convexity of X*: Every equivalent norm on X is Fréchet differentiable on a dense set if and only if X* has the RNP. A more general measure of convexity has been recently receiving a great deal of attention: A dual Banach space X* has the weak* Convex Point-of-Continuity Property (C*PCP) if whenever ɸ ≠ C ⊂ X* is weak*-compact and convex, and ∈ > 0, there is a weak*-open set V such that V ⋂ C ≠ ɸ and diam V ⋂ C < ∈. In this thesis, we develop the corresponding smoothness properties of X which are dual to C*PCP. For this, a new type of differentiability, called cofinite Fréchet differentiability, is introduced, and we establish the following theorem: Every equivalent norm on X is cofinitely Fréchet differentiable everywhere if and only if X* has the C*PCP. Representing joint work with R. Deville, G. Godefroy and V. Zizler, an alternate approach is developed in the case when X is separable. We show that if X is separable, then every equivalent norm on X which has a strictly convex dual is Fréchet differentiable on a dense set if and only if X* has the C*PCP, if and only if every equivalent norm on X which is Gâteaux differentiable (everywhere) is Fréchet differentiable on a dense set. This result is used to show that if X* does not have the C*PCP, then there is a subspace Y of X such that neither Y* nor (X/Y)* have the C*PCP, yet both Y and X/Y have finite dimensional Schauder decompositions. The corresponding result for spaces X* failing the RNP remains open.
Science, Faculty of
Mathematics, Department of
Graduate
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Freund, Robert M., and Fernando 1970 Ordóñez. "On an Extension of Condition Number Theory to Non-Conic Convex Optimization." Massachusetts Institute of Technology, Operations Research Center, 2003. http://hdl.handle.net/1721.1/5404.

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The purpose of this paper is to extend, as much as possible, the modern theory of condition numbers for conic convex optimization: z* := minz ctx s.t. Ax - b Cy C Cx , to the more general non-conic format: z* := minx ctx (GPd) s.t. Ax-b E Cy X P, where P is any closed convex set, not necessarily a cone, which we call the groundset. Although any convex problem can be transformed to conic form, such transformations are neither unique nor natural given the natural description of many problems, thereby diminishing the relevance of data-based condition number theory. Herein we extend the modern theory of condition numbers to the problem format (GPd). As a byproduct, we are able to state and prove natural extensions of many theorems from the conic-based theory of condition numbers to this broader problem format.
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Yu, Haofeng. "A Numerical Investigation Of The Canonical Duality Method For Non-Convex Variational Problems." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/29095.

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This thesis represents a theoretical and numerical investigation of the canonical duality theory, which has been recently proposed as an alternative to the classic and direct methods for non-convex variational problems. These non-convex variational problems arise in a wide range of scientific and engineering applications, such as phase transitions, post-buckling of large deformed beam models, nonlinear field theory, and superconductivity. The numerical discretization of these non-convex variational problems leads to global minimization problems in a finite dimensional space. The primary goal of this thesis is to apply the newly developed canonical duality theory to two non-convex variational problems: a modified version of Ericksen's bar and a problem of Landau-Ginzburg type. The canonical duality theory is investigated numerically and compared with classic methods of numerical nature. Both advantages and shortcomings of the canonical duality theory are discussed. A major component of this critical numerical investigation is a careful sensitivity study of the various approaches with respect to changes in parameters, boundary conditions and initial conditions.
Ph. D.
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Csetnek, Ernö Robert. "Overcoming the failure of the classical generalized interior-point regularity conditions in convex optimization. Applications of the duality theory to enlargements of maximal monotone operators." Doctoral thesis, Universitätsbibliothek Chemnitz, 2009. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200902025.

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The aim of this work is to present several new results concerning duality in scalar convex optimization, the formulation of sequential optimality conditions and some applications of the duality to the theory of maximal monotone operators. After recalling some properties of the classical generalized interiority notions which exist in the literature, we give some properties of the quasi interior and quasi-relative interior, respectively. By means of these notions we introduce several generalized interior-point regularity conditions which guarantee Fenchel duality. By using an approach due to Magnanti, we derive corresponding regularity conditions expressed via the quasi interior and quasi-relative interior which ensure Lagrange duality. These conditions have the advantage to be applicable in situations when other classical regularity conditions fail. Moreover, we notice that several duality results given in the literature on this topic have either superfluous or contradictory assumptions, the investigations we make offering in this sense an alternative. Necessary and sufficient sequential optimality conditions for a general convex optimization problem are established via perturbation theory. These results are applicable even in the absence of regularity conditions. In particular, we show that several results from the literature dealing with sequential optimality conditions are rediscovered and even improved. The second part of the thesis is devoted to applications of the duality theory to enlargements of maximal monotone operators in Banach spaces. After establishing a necessary and sufficient condition for a bivariate infimal convolution formula, by employing it we equivalently characterize the $\varepsilon$-enlargement of the sum of two maximal monotone operators. We generalize in this way a classical result concerning the formula for the $\varepsilon$-subdifferential of the sum of two proper, convex and lower semicontinuous functions. A characterization of fully enlargeable monotone operators is also provided, offering an answer to an open problem stated in the literature. Further, we give a regularity condition for the weak$^*$-closedness of the sum of the images of enlargements of two maximal monotone operators. The last part of this work deals with enlargements of positive sets in SSD spaces. It is shown that many results from the literature concerning enlargements of maximal monotone operators can be generalized to the setting of Banach SSD spaces.
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Calisti, Matteo. "Differential calculus in metric measure spaces." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21781/.

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L'obbiettivo di questa tesi è la definizione del calcolo differenziale e dell'operatore di Laplace in spazi metrici di misura. Nel primo capitolo vengono introdotte le definizioni e proprietà principali degli spazi metrici di misura mentre nel secondo quelle riguardanti le funzioni lipschitziane e la derivata metrica di curve assolutamente continue. Nel terzo capitolo quindi viene definito il concetto di p-supergradiente debole e di conseguenza la classe di Sobolev S^p. Nel quarto capitolo viene poi studiata la generalizzazione del concetto di differenziale di f applicato al gradiente di g che da luogo a due funzioni che in generale risultano diverse, ma se coincidono lo spazio verrà detto q-infinitesimamente strettamente convesso. Vengono quindi dimostrate alcune regole della catena per per queste due funzioni attraverso la dualità fra lo spazio S^p e un opportuno spazio di misure dette q-piani test. In particolare mediante l'introduzione del funzionale energia di Cheeger e il suo flusso-gradiente sarà possibile associare un piano di trasporto al gradiente di una funzione in S^p. Nel quinto capitolo viene definito il p-laplaciano e le regole di calcolo provate precedentemente saranno usate per provare quelle per il laplaciano. Verranno poi definiti gli spazi infitesimamente di Hilbert: in questo caso il laplaciano assume un solo valore e risulta linearmente dipendente da g e si dimostra un'identificazione tra differenziali e gradienti. Nell'ultima parte del quinto capitolo infine viene mostrata un'applicazione del calcolo differenziale in spazi metrici di misura al gruppo di Heisenberg, considerandolo uno spazio metrico di misura munito della metrica di Korany e la misura di Lebesgue. Nella prima parte si mostra che il laplaciano metrico coincide con quello subriemanniano. Viene poi considerata nella seconda parte la sottovarietà {x=0} e si dimostra come il laplaciano metrico sia diverso da quello differenziale.
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"Duality theory, saddle point problem and vector optimization in distributed systems." Chinese University of Hong Kong, 1985. http://library.cuhk.edu.hk/record=b5885566.

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"Duality theory by sum of epigraphs of conjugate functions in semi-infinite convex optimization." 2009. http://library.cuhk.edu.hk/record=b5894114.

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Lau, Fu Man.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2009.
Includes bibliographical references (leaves 94-97).
Abstract also in Chinese.
Abstract --- p.i
Acknowledgements --- p.iii
Chapter 1 --- Introduction --- p.1
Chapter 2 --- Notations and Preliminaries --- p.4
Chapter 2.1 --- Introduction --- p.4
Chapter 2.2 --- Basic notations --- p.4
Chapter 2.3 --- On the properties of subdifferentials --- p.8
Chapter 2.4 --- On the properties of normal cones --- p.9
Chapter 2.5 --- Some computation rules for conjugate functions --- p.13
Chapter 2.6 --- On the properties of epigraphs --- p.15
Chapter 2.7 --- Set-valued analysis --- p.19
Chapter 2.8 --- Weakly* sum of sets in dual spaces --- p.21
Chapter 3 --- Sum of Epigraph Constraint Qualification (SECQ) --- p.31
Chapter 3.1 --- Introduction --- p.31
Chapter 3.2 --- Definition of the SECQ and its basic properties --- p.33
Chapter 3.3 --- Relationship between the SECQ and other constraint qualifications --- p.39
Chapter 3.3.1 --- The SECQ and the strong CHIP --- p.39
Chapter 3.3.2 --- The SECQ and the linear regularity --- p.46
Chapter 3.4 --- Interior-point conditions for the SECQ --- p.58
Chapter 3.4.1 --- I is finite --- p.59
Chapter 3.4.2 --- I is infinite --- p.61
Chapter 4 --- Duality theory of semi-infinite optimization via weakly* sum of epigraph of conjugate functions --- p.70
Chapter 4.1 --- Introduction --- p.70
Chapter 4.2 --- Fenchel duality in semi-infinite convex optimization --- p.73
Chapter 4.3 --- Sufficient conditions for Fenchel duality in semi-infinite convex optimization --- p.79
Chapter 4.3.1 --- Continuous real-valued functions --- p.80
Chapter 4.3.2 --- Nonnegative-valued functions --- p.84
Bibliography --- p.94
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Books on the topic "Convex duality theory"

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service), SpringerLink (Online, ed. Conjugate Duality in Convex Optimization. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2010.

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Duality in nonconvex approximation and optimization. New York: Springer, 2005.

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Șandru, Ovidiu-Ilie. Noneuclidean convexity: Applications in the programming theory. București: Editura Tehnică, 1998.

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Gao, David Yang. Duality principles in nonconvex systems: Theory, methods, and applications. Dordrecht: Kluwer Academic Publishers, 2000.

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Guédon, Olivier. Analytical and probabilistic methods in the geometry of convex bodies. Warszawa: Institute of Mathematics, Polish Academy of Sciences, 2014.

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1929-, Ponstein Jacob, ed. Convexity and duality in optimization: Proceedings of the Symposium on Convexity and Duality in Optimization held at the University of Groningen, the Netherlands, June 22, 1984. Berlin: Springer-Verlag, 1985.

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Nonsmooth mechanics and convex optimization. Boca Raton, FL: CRC Press/Taylor & Francis, 2011.

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Drigojias, Ioannis. Approximationseigenschaft und Dualität von gewichteten H⁽p̳⁾- Räumen. [Münster]: Drucktechnische Zentralstelle der Universität Münster, 1993.

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Singer, Ivan. Duality for Nonconvex Approximation and Optimization (CMS Books in Mathematics). Springer, 2006.

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Grad, Sorin-Mihai. Vector Optimization and Monotone Operators via Convex Duality: Recent Advances. Springer, 2016.

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Book chapters on the topic "Convex duality theory"

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Güler, Osman. "Duality Theory and Convex Programming." In Foundations of Optimization, 275–312. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-0-387-68407-9_11.

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Altun, Yasemin, and Alex Smola. "Unifying Divergence Minimization and Statistical Inference Via Convex Duality." In Learning Theory, 139–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11776420_13.

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Oliveira, Rúbia M., and Paulo A. V. Ferreira. "Global Optimization of Convex Multiplicative Programs by Duality Theory." In Global Optimization and Constraint Satisfaction, 101–11. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11425076_8.

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Boţ, Radu Ioan, and Gert Wanka. "Duality for composed convex functions with applications in location theory." In Multi-Criteria- und Fuzzy-Systeme in Theorie und Praxis, 1–18. Wiesbaden: Deutscher Universitätsverlag, 2003. http://dx.doi.org/10.1007/978-3-322-81539-2_1.

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Hiriart-Urruty, Jean-Baptiste, and Claude Lemaréchal. "Constrained Convex Minimization Problems: Minimality Conditions, Elements of Duality Theory." In Grundlehren der mathematischen Wissenschaften, 291–341. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-662-02796-7_7.

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Frenk, J. G. B., D. M. L. Dias, and J. Gromicho. "Duality theory for convex/quasiconvex functions and its application to optimization." In Lecture Notes in Economics and Mathematical Systems, 153–70. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-46802-5_14.

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Glückler, Johannes. "Lateral Network Governance." In Knowledge for Governance, 243–65. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-47150-7_11.

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AbstractThe author of this article goes beyond acknowledging networks as a governance mode to elaborate on the actual forms of governance that convey legitimate and acceptable coordination. He advances the concept of lateral network governance in the empirical context of organized networks, in which organizations pool resources and join their interests in the pursuit of common goals. To solve the puzzle of having independent equals commit themselves to coordinating their actions, the author aims to overcome the traditional dualism between formal and informal mechanisms of governance. Instead, he conceives lateral network governance as a structure for the legitimate delegation of decision-making. He develops a social network analytic approach to assessing the relational distribution of legitimacy. With his empirical analysis of two case studies of inter-firm network organizations, he illustrates the degree to which the actual legitimacy distribution diverges from formal governance authority. Lateral network governance has practical implications for inter-organizational networks and network managers.
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Cohen, Liron. "Non-well-founded Deduction for Induction and Coinduction." In Automated Deduction – CADE 28, 3–24. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79876-5_1.

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AbstractInduction and coinduction are both used extensively within mathematics and computer science. Algebraic formulations of these principles make the duality between them apparent, but do not account well for the way they are commonly used in deduction. Generally, the formalization of these reasoning methods employs inference rules that express a general explicit (co)induction scheme. Non-well-founded proof theory provides an alternative, more robust approach for formalizing implicit (co)inductive reasoning. This approach has been extremely successful in recent years in supporting implicit inductive reasoning, but is not as well-developed in the context of coinductive reasoning. This paper reviews the general method of non-well-founded proofs, and puts forward a concrete natural framework for (co)inductive reasoning, based on (co)closure operators, that offers a concise framework in which inductive and coinductive reasoning are captured as we intuitively understand and use them. Through this framework we demonstrate the enormous potential of non-well-founded deduction, both in the foundational theoretical exploration of (co)inductive reasoning and in the provision of proof support for (co)inductive reasoning within (semi-)automated proof tools.
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9

Botelho, Fabio Silva. "Convex Analysis and Duality Theory." In Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering, 296–327. CRC Press, 2020. http://dx.doi.org/10.1201/9780429343315-16.

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10

"Convex duality theory for optimal investment." In AMS/IP Studies in Advanced Mathematics, 663–78. Providence, Rhode Island: American Mathematical Society, 2008. http://dx.doi.org/10.1090/amsip/042.2/16.

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Conference papers on the topic "Convex duality theory"

1

Nielsen, Sue, Liisa von Hellens, and Jenine Beekhuyzen. "Challenge or Chaos: A Discourse Analysis of W omen’s Perceptions of the Culture of Change in the IT Industry." In InSITE 2004: Informing Science + IT Education Conference. Informing Science Institute, 2004. http://dx.doi.org/10.28945/2760.

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Abstract:
An ongoing investigation into the declining participation of women in IT education and professional level work has recently focused on professional women’s perceptions of the IT industry. This paper presents some of the findings from a discourse analysis of interviews with thirty-two female and two male IT professionals. The analysis identified a distinctive characteristic of the women’s discourse in the representation of mutually exclusive attributes, skills and attitudes as closely identified with gender. This paper explores two of these dualisms - women’s perceptions of the rapid and continuous change characteristic of the IT industry and the dualism of the public (work) and private (domestic) spheres. The implications of rapid change and the concomitant long working hours characteristic of the IT industry, are discussed in relation to women’s continued responsibility for social and domestic life. Discourse analysis is used to identify contradictions in the women’s talk and to relate this to tensions in the IT industry and the wider social context. Although these women characterise themselves as ‘different’ from most women, in their skills, aptitudes and attitudes towards IT, this characterisation shows tensions and contradictions. The authors use Giddens’ perspective on identity formation and the structuration of institutions (Giddens, 1984; 1991) to identify factors, which may further discourage women from participating in IT education and work.
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