Conjugate Duality in Convex Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Conjugate Duality in Convex Optimization write by Radu Ioan Bot. This book was released on 2009-12-24. Conjugate Duality in Convex Optimization available in PDF, EPUB and Kindle. The results presented in this book originate from the last decade research work of the author in the ?eld of duality theory in convex optimization. The reputation of duality in the optimization theory comes mainly from the major role that it plays in formulating necessary and suf?cient optimality conditions and, consequently, in generatingdifferent algorithmic approachesfor solving mathematical programming problems. The investigations made in this work prove the importance of the duality theory beyond these aspects and emphasize its strong connections with different topics in convex analysis, nonlinear analysis, functional analysis and in the theory of monotone operators. The ?rst part of the book brings to the attention of the reader the perturbation approach as a fundamental tool for developing the so-called conjugate duality t- ory. The classical Lagrange and Fenchel duality approaches are particular instances of this general concept. More than that, the generalized interior point regularity conditions stated in the past for the two mentioned situations turn out to be p- ticularizations of the ones given in this general setting. In our investigations, the perturbationapproachrepresentsthestartingpointforderivingnewdualityconcepts for several classes of convex optimization problems. Moreover, via this approach, generalized Moreau–Rockafellar formulae are provided and, in connection with them, a new class of regularity conditions, called closedness-type conditions, for both stable strong duality and strong duality is introduced. By stable strong duality we understand the situation in which strong duality still holds whenever perturbing the objective function of the primal problem with a linear continuous functional.
Conjugate Duality and Optimization
Conjugate Duality and Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Conjugate Duality and Optimization write by R. Tyrrell Rockafellar. This book was released on 1974-01-01. Conjugate Duality and Optimization available in PDF, EPUB and Kindle. The theory of duality in problems of optimization is developed in a setting of finite and infinite dimensional spaces using convex analysis. Applications to convex and nonconvex problems. Expository account containing many new results. (Author).
Convex Duality and Financial Mathematics
Convex Duality and Financial Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Convex Duality and Financial Mathematics write by Peter Carr. This book was released on 2018-07-18. Convex Duality and Financial Mathematics available in PDF, EPUB and Kindle. This book provides a concise introduction to convex duality in financial mathematics. Convex duality plays an essential role in dealing with financial problems and involves maximizing concave utility functions and minimizing convex risk measures. Recently, convex and generalized convex dualities have shown to be crucial in the process of the dynamic hedging of contingent claims. Common underlying principles and connections between different perspectives are developed; results are illustrated through graphs and explained heuristically. This book can be used as a reference and is aimed toward graduate students, researchers and practitioners in mathematics, finance, economics, and optimization. Topics include: Markowitz portfolio theory, growth portfolio theory, fundamental theorem of asset pricing emphasizing the duality between utility optimization and pricing by martingale measures, risk measures and its dual representation, hedging and super-hedging and its relationship with linear programming duality and the duality relationship in dynamic hedging of contingent claims
Duality in Vector Optimization
Duality in Vector Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Duality in Vector Optimization write by Radu Ioan Bot. This book was released on 2009-08-12. Duality in Vector Optimization available in PDF, EPUB and Kindle. This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. One chapter is exclusively consecrated to the scalar and vector Wolfe and Mond-Weir duality schemes.
Overcoming the Failure of the Classical Generalized Interior-point Regularity Conditions in Convex Optimization
Overcoming the Failure of the Classical Generalized Interior-point Regularity Conditions in Convex Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Overcoming the Failure of the Classical Generalized Interior-point Regularity Conditions in Convex Optimization write by Ernö Robert Csetnek. This book was released on 2010-06-30. Overcoming the Failure of the Classical Generalized Interior-point Regularity Conditions in Convex Optimization available in PDF, EPUB and Kindle. 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 en.
