A note on approximate Karush–Kuhn–Tucker conditions in locally Lipschitz multiobjective optimization

Optimality Conditions for Approximate Solutions in Multiobjective Optimization Problems

We study firstand second-order necessary and sufficient optimality conditions for approximate weakly, properly efficient solutions of multiobjective optimization problems. Here, tangent cone, -normal cone, cones of feasible directions, second-order tangent set, asymptotic second-order cone, and Hadamard upper lower directional derivatives are used in the characterizations. The results are first...

The proximal point method for locally Lipschitz functions in multiobjective optimization

This paper studies the constrained multiobjective optimization problem of finding Pareto critical points of vector-valued functions. The proximal point method considered by Bonnel et al. (SIAM J. Optim., 4 (2005), pp. 953-970) is extended to locally Lipschitz functions in the finite dimensional multiobjective setting. To this end, a new approach for convergence analysis of the method is propose...

An effective optimization algorithm for locally nonconvex Lipschitz functions based on mollifier subgradients

A Note on Multiobjective Optimization and Complementarity Constraints∗

We propose a new approach to convex nonlinear multiobjective optimization that captures the geometry of the Pareto set by generating a discrete set of Pareto points optimally. We show that the problem of finding an optimal representation of the Pareto surface can be formulated as a mathematical program with complementarity constraints. The complementarity constraints arise from modeling the set...

Sequential Approximate Multiobjective Optimization Using Computational Intelligence

In many practical problems, in particular in engineering design, the function form of criteria is not given explicitly in terms of design variables. Given the value of design variables, under this circumstance, the value of objective functions is obtained by real/computational experiments such as structural analysis, fluidmechanic analysis, thermodynamic analysis, and so on. Usually, these expe...