On Optimality and Duality Theory for Optimization Problems

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dual model corresponding to given primal problems and some duality results were piled up in Section 1.4. In Section 1.5, we recall standard minimax programming problem and present a small overview on the same. In Section 1.6, we introduce a short note on saddle point optimality problems. In Section 1.7, we present basic concept of multiobjective optimization problems and its solutions. Section 1.8 recalls constraint qualification in multiobjective optimization problems. In Section 1.9, scalar and multiobjective semi-infinite optimization problems is introduced. In Section 1.10, we remind definitions of Lipschitz and locally Lipschitz continuity. Section 1.11 presents definition, basic properties of convexificators and recalls generalized convexity in terms of convexificators. Sections 1.12 is all about brief literature on semidefinite programming problem and related concepts for further use. Section 1.13 presents short introduction on vector variational inequality. Finally, Section 1.14 includes basic details of mathematical programming with vanishing constraints and its literature.