Saddle Point and Second Order Optimality in Nondifferentiable Nonlinear Abstract Multiobjective Optimization

Abstract

Abstract. This article deals with a vector optimization problem with cone constraints in a Banach space setting. By making use of a real-valued Lagrangian and the concept of generalized subconvex-like functions, weakly efficient solutions are characterized through saddle point type conditions. The results, jointly with the notion of generalized Hessian (introduced in [Cominetti, R., Correa, R.: A generalized second-order derivative in nonsmooth optimization. SIAM J. Control Optim. 28, 789-809 (1990)]), are applied to achieve second order necessary and sufficient optimality conditions (without requiring twice differentiability for the objective and constraining functions) for the particular case when the functionals involved are defined on a general Banach space into finite dimensional ones.

On Modified Interval-Valued Variational Control Problems with First-Order PDE Constraints

“…In recent years, saddle-point optimality criteria and the modified objective function method in optimization problems have been investigated. In this regard, we mention the works of Sposito and David [1], Smith and Vandelinde [2], Duc et al [3], Li [4] and Santos et al [5]. In order to solve the initial optimization problem and the corresponding duals, many researchers have been interested in obtaining new and easier methods by considering some associated optimization problems.…”