Relevant bibliographies by topics / Convex Function and Duality

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
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Academic literature on the topic 'Convex Function and Duality'

Author: Grafiati
Published: 4 June 2025
Last updated: 1 August 2025

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Journal articles on the topic "Convex Function and Duality"

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Egudo, Richard R. "Multiobjective fractional duality." Bulletin of the Australian Mathematical Society 37, no. 3 (1988): 367–78. http://dx.doi.org/10.1017/s0004972700026988.

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The concept of efficiency (Pareto optimum) is used to formulate duality for multiobjective fractional programming problems. We consider programs where the components of the objective function have non-negative and convex numerators while the denominators are concave and positive. For this case the Mond-Weir extension of Bector dual analogy is given. We also give the Schaible type vector dual. The case where functions are ρ-convex (weakly or strongly convex) is also considered.
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Wibowo, Ratno Bagus Edy, Marjono, and Eko Dedi Pramana. "Legendre-Fenchel duality in m-convexity." Hilbert Journal of Mathematical Analysis 2, no. 2 (2024): 099–105. http://dx.doi.org/10.62918/hjma.v2i2.23.

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Zhang, Jun. "Divergence Function, Duality, and Convex Analysis." Neural Computation 16, no. 1 (2004): 159–95. http://dx.doi.org/10.1162/08997660460734047.

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From a smooth, strictly convex function Φ: Rn → R, a parametric family of divergence function DΦ(α) may be introduced: [Formula: see text] for x, y, ε int dom(Φ) and for α ε R, with DΦ(±1 defined through taking the limit of α. Each member is shown to induce an α-independent Riemannian metric, as well as a pair of dual α-connections, which are generally nonflat, except for α = ±1. In the latter case, D(±1)Φ reduces to the (nonparametric) Bregman divergence, which is representable using and its convex conjugate Φ * and becomes the canonical divergence for dually flat spaces (Amari, 1982, 1985; A
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Hassan, Mansur, and Adam Baharum. "Modified Courant-Beltrami penalty function and a duality gap for invex optimization problem." International Journal for Simulation and Multidisciplinary Design Optimization 10 (2019): A10. http://dx.doi.org/10.1051/smdo/2019010.

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In this paper, we modified a Courant-Beltrami penalty function method for constrained optimization problem to study a duality for convex nonlinear mathematical programming problems. Karush-Kuhn-Tucker (KKT) optimality conditions for the penalized problem has been used to derived KKT multiplier based on the imposed additional hypotheses on the constraint function g. A zero-duality gap between an optimization problem constituted by invex functions with respect to the same function η and their Lagrangian dual problems has also been established. The examples have been provided to illustrate and pr
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Scott, C. H., T. R. Jefferson, and E. Sirri. "On duality for convex minimization with nested maxima." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 26, no. 4 (1985): 517–22. http://dx.doi.org/10.1017/s0334270000004690.

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AbstractIn this paper, we consider convex programs with linear constraints where the objective function involves nested maxima of linear functions as well as a convex function. A dual program is constructed which has interpretational significance and may be easier to solve than the primal formulation. A numerical example is given to illustrate the method.
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Kailey, N., and S. Sonali. "Higher-order symmetric duality in nondifferentiable multiobjective optimization over cones." Filomat 33, no. 3 (2019): 711–24. http://dx.doi.org/10.2298/fil1903711k.

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In this paper, a new pair of higher-order nondifferentiable multiobjective symmetric dual programs over arbitrary cones is formulated, where each of the objective functions contains a support function of a compact convex set. We identify a function lying exclusively in the class of higher-order K-?-convex and not in the class of K-?-bonvex function already existing in literature. Weak, strong and converse duality theorems are then established under higher-order K-?-convexity assumptions. Self duality is obtained by assuming the functions involved to be skew-symmetric. Several known results are
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Mishra, M. S., S. Nanda, and D. Acharya. "Strong pseudo-convexity and symmetric duality in nonlinear programming." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 27, no. 2 (1985): 238–44. http://dx.doi.org/10.1017/s0334270000004884.

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AbstractIn this note, the weak duality theorem of symmetric duality in nonlinear programming and some related results are established under weaker (strongly Pseudo-convex/strongly Pseudo-concave) assumptions. These results were obtained by Bazaraa and Goode [1] under (stronger) convex/concave assumptions on the function.
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Fang, D. H. "Stable Zero Lagrange Duality for DC Conic Programming." Journal of Applied Mathematics 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/606457.

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We consider the problems of minimizing a DC function under a cone-convex constraint and a set constraint. By using the infimal convolution of the conjugate functions, we present a new constraint qualification which completely characterizes the Farkas-type lemma and the stable zero Lagrange duality gap property for DC conical programming problems in locally convex spaces.
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Dubey, Ramu, and S. K. Gupta. "On duality for a second-order multiobjective fractional programming problem involving type-I functions." Georgian Mathematical Journal 26, no. 3 (2019): 393–404. http://dx.doi.org/10.1515/gmj-2017-0038.

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Abstract The purpose of this paper is to study a nondifferentiable multiobjective fractional programming problem (MFP) in which each component of objective functions contains the support function of a compact convex set. For a differentiable function, we introduce the class of second-order {(C,\alpha,\rho,d)-V} -type-I convex functions. Further, Mond–Weir- and Wolfe-type duals are formulated for this problem and appropriate duality results are proved under the aforesaid assumptions.
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Volle, M., J. E. Martínez-Legaz, and J. Vicente-Pérez. "Duality for Closed Convex Functions and Evenly Convex Functions." Journal of Optimization Theory and Applications 167, no. 3 (2013): 985–97. http://dx.doi.org/10.1007/s10957-013-0395-4.

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Dissertations / Theses on the topic "Convex Function and Duality"

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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
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Hodrea, Ioan Bogdan. "Farkas - type results for convex and non - convex inequality systems." Doctoral thesis, [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800075.

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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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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
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Bot, Radu Ioan. "Duality and optimality in multiobjective optimization." Doctoral thesis, Universitätsbibliothek Chemnitz, 2003. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200300842.

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The aim of this work is to make some investigations concerning duality for multiobjective optimization problems. In order to do this we study first the duality for scalar optimization problems by using the conjugacy approach. This allows us to attach three different dual problems to a primal one. We examine the relations between the optimal objective values of the duals and verify, under some appropriate assumptions, the existence of strong duality. Closely related to the strong duality we derive the optimality conditions for each of these three duals. By means of these considerations, we stud
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Boţ, Radu Ioan. "Conjugate duality in convex optimization." Berlin [u.a.] Springer, 2010. http://dx.doi.org/10.1007/978-3-642-04900-2.

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Tünde, Vargyas Emese. "Duality for convex composed programming problems." [S.l. : s.n.], 2004. http://archiv.tu-chemnitz.de/pub/2004/0179.

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ROCCO, Marco. "Maximal Monotone Operators, Convex Representations and Duality." Doctoral thesis, Università degli studi di Bergamo, 2011. http://hdl.handle.net/10446/869.

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Tsoutsinos, George. "Convex duality in control problems with time-delays." Thesis, Imperial College London, 1990. http://hdl.handle.net/10044/1/46587.

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Kim, Jaegil. "Duality phenomena and Volume inequalities in Convex Geometry." Kent State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=kent1368188809.

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Books on the topic "Convex Function and Duality"

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

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Panik, Michael J. Fundamentals of convex analysis: Duality, separation, representation, and resolution. Kluwer Academic Publishers, 1993.

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1941-, Cambini A., Dass B. K. 1951-, and Martein L. 1952-, eds. Generalized convexity, generalized monotonicity, optimality conditions, and duality in scaler and vector optimization. Taru Publications and Academic Forum, Delhi, 2003.

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Carr, Peter, and Qiji Jim Zhu. Convex Duality and Financial Mathematics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-92492-2.

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Bot, Radu Ioan. Conjugate Duality in Convex Optimization. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-04900-2.

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Grad, Sorin-Mihai. Vector Optimization and Monotone Operators via Convex Duality. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-08900-3.

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

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

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Gao, David Yang. Duality Principles in Nonconvex Systems: Theory, Methods and Applications. Springer US, 2000.

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10

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

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Book chapters on the topic "Convex Function and Duality"

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Tao, Pham Dinh, and El Bernoussi Souad. "Duality in D.C. (Difference of Convex functions) Optimization. Subgradient Methods." In Trends in Mathematical Optimization. Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-9297-1_18.

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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. Deutscher Universitätsverlag, 2003. http://dx.doi.org/10.1007/978-3-322-81539-2_1.

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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. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-46802-5_14.

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Hiriart-Urruty, J. B. "Generalized Differentiability / Duality and Optimization for Problems Dealing with Differences of Convex Functions." In Lecture Notes in Economics and Mathematical Systems. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-45610-7_3.

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Amari, Shun-ichi. "Information Geometry and Its Applications: Convex Function and Dually Flat Manifold." In Emerging Trends in Visual Computing. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00826-9_4.

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Carr, Peter, and Qiji Jim Zhu. "Convex Duality." In SpringerBriefs in Mathematics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-92492-2_1.

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Aliprantis, Charalambos, and Rabee Tourky. "Piecewise affine functions." In Cones and Duality. American Mathematical Society, 2007. http://dx.doi.org/10.1090/gsm/084/07.

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Ekeland, Ivar. "Non-Convex Duality." In Advances in Mechanics and Mathematics. Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-90-481-9577-0_2.

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Borwein, Jonathan M., and Adrian S. Lewis. "Fenchel Duality." In Convex Analysis and Nonlinear Optimization. Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4757-9859-3_3.

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Bauschke, Heinz H., and Patrick L. Combettes. "Duality in Convex Optimization." In CMS Books in Mathematics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-48311-5_19.

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Conference papers on the topic "Convex Function and Duality"

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Jang, JaeIl, Da Hwi Kim, and Chang-Hun Lee. "Powered Descent Guidance via Sequential Convex Programming with Constraint Function Design." In 2025 IEEE Aerospace Conference. IEEE, 2025. https://doi.org/10.1109/aero63441.2025.11068579.

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Pakniyat, Ali. "Distributionally Constrained Convex Duality Optimal Control (DC-CDOC) Subject to Different Forms of Constraining the Terminal State of Nonlinear Stochastic Systems." In 2024 IEEE 63rd Conference on Decision and Control (CDC). IEEE, 2024. https://doi.org/10.1109/cdc56724.2024.10885913.

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Alçalar, Yaşar Utku, Merve Gülle, and Mehmet Akçakaya. "A Convex Compressibility-Inspired Unsupervised Loss Function for Physics-Driven Deep Learning Reconstruction." In 2024 IEEE International Symposium on Biomedical Imaging (ISBI). IEEE, 2024. http://dx.doi.org/10.1109/isbi56570.2024.10635138.

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Eising, Jaap, and M. Kanat Camlibel. "On Duality for Lyapunov Functions of Nonstrict Convex Processes." In 2020 59th IEEE Conference on Decision and Control (CDC). IEEE, 2020. http://dx.doi.org/10.1109/cdc42340.2020.9304205.

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Ying-ying, Wang, and Luo Rui-ping. "Duality Theorems of Multiobjective Programming for a Class of Generalized Convex Functions." In 2007 International Conference on Management Science and Engineering. IEEE, 2007. http://dx.doi.org/10.1109/icmse.2007.4421909.

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Thirugnanam, Akshay, Jun Zeng, and Koushil Sreenath. "Duality-based Convex Optimization for Real-time Obstacle Avoidance between Polytopes with Control Barrier Functions." In 2022 American Control Conference (ACC). IEEE, 2022. http://dx.doi.org/10.23919/acc53348.2022.9867246.

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Briales, Jesus, and Javier Gonzalez-Jimenez. "Convex Global 3D Registration with Lagrangian Duality." In 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2017. http://dx.doi.org/10.1109/cvpr.2017.595.

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Cole, Richard, Nikhil Devanur, Vasilis Gkatzelis, et al. "Convex Program Duality, Fisher Markets, and Nash Social Welfare." In EC '17: ACM Conference on Economics and Computation. ACM, 2017. http://dx.doi.org/10.1145/3033274.3085109.

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Sağlam, Sevilay Demir, and Elimhan N. Mahmudov. "The duality of convex optimization problem for differential inclusions." In 10TH INTERNATIONAL CONFERENCE ON APPLIED SCIENCE AND TECHNOLOGY. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0117079.

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Christophe, Franc¸ois, Tuomas Ritola, Eric Coatane´a, and Alain Bernard. "Semantic Analysis of Function-Solution Duality." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-63546.

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Methodologies of the literature tend to separate clearly the design problem definition from the solutions to this problem. Nevertheless, this paper argues that conceptual design solutions are deeply rooted in the definition of the design problem. Hence, it is shown that conceptual solutions can emerge from the semantic analysis of the functional definition of a problem. This paper addresses the recursive aspect of conceptual design and the iterative loops between each step of design methodologies which are usually presented as a sequential flow. This paper presents that, in fact, in the early
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Reports on the topic "Convex Function and Duality"

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Fleming, Wendell H., and Domokos Vermes. Convex Duality Approach to the Optimal Control or Diffusions,. Defense Technical Information Center, 1988. http://dx.doi.org/10.21236/ada194535.

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Mushtaq, Saima, Mohsan Raza, and Wasim ul Haq. Sufficient Conditions for a Meromorphic Function to Be p-valent Starlike or Convex. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, 2019. http://dx.doi.org/10.7546/crabs.2019.12.01.

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Bai, Z. D., C. R. Rao, and L. C. Zhao. MANOVA Type Tests Under a Convex Discrepancy Function for the Standard Multivariate Linear Model. Defense Technical Information Center, 1993. http://dx.doi.org/10.21236/ada271031.

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