We consider vector optimization problems on Banach spaces without convexity assumptions. Under the assumption that the objective function is locally Lipschitz we derive Lagrangian necessary conditions on the basis of Mordukhovich subdifferential and the approximate subdifferential by Ioffe using...

We consider vector optimization problems on Banach spaces without convexity assumptions. Under the assumption that the objective function is locally Lipschitz we derive Lagrangian necessary conditions on the basis of Mordukhovich subdifferential and the approximate subdifferential by Ioffe using...

In solving certain optimization problems, the corresponding Lagrangian dual problem is often solved simply because in these problems the dual problem is easier to solve than the original primal problem. Another reason for their solution is the implication of the weak duality theorem which...

Karush–Kuhn–Tucker (KKT) optimality conditions are often checked for investigating whether a solution obtained by an optimization algorithm is a likely candidate for the optimum. In this study, we report that although the KKT conditions must all be satisfied at the optimal point, the extent...

Introduction -- Sets and Binary Relations -- Extended Real-Valued Functions -- Translation Invariant Functions -- Minimizers of Translation Invariant Functions -- Vector Optimization in General Spaces -- Multiobjective Optimization -- Variational Analysis -- Special Cases and Functionals Related...