On Optimality and Duality Theory for Optimization Problems

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