Conjugate Duality in Convex Optimization

"Conjugate Duality in Convex Optimization" is a technical book that presents the results of the author's research over the past ten years in the field of duality theory in convex optimization. Duality plays a central role in formulating necessary and sufficient optimality conditions and is crucial for the development of various algorithmic approaches to solving mathematical programming problems. This book goes beyond the traditional aspects of duality and highlights its strong connections to various topics in convex analysis, nonlinear analysis, functional analysis, and the theory of monotone operators. The first part of the book introduces the perturbation approach as a fundamental tool for developing the so-called conjugate duality theory. The classical Lagrange and Fenchel duality approaches are viewed as special cases of this general concept. Furthermore, new duality concepts for different classes of convex optimization problems are derived, emphasizing the relevance and applicability of duality theory.