On Optimality and Duality Theory for Optimization Problems

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.