On approximate solutions for robust semi-infinite multi-objective convex symmetric cone optimization

We present approximate solutions for the robust semi-infinite multi-objective convex symmetric cone programming problem. By using the robust optimization approach, we establish an approximate optimality theorem and approximate duality theorems for approximate solutions in convex symmetric cone optimization problem involving infinitely many constraints to be satisfied and multiple objectives to be optimized simultaneously under the … Read more

Global Optimization via Slack Variables

This paper presents a method for finding global optima to constrained nonlinear programs via slack variables. The method only applies if all functions involved are of class C1 but without any further qualification on the types of constraints allowed; it proceeds by reformulating the given program into a bi-objective program that is then solved for … Read more

Practical Multi-objective Programming

This paper is on practical solutions to the multi-objective optimization problem; it advocates for single-point solutions either of the Nash equilibrium or the Tchebycheff compromise type, depending on whether one can reasonably ascribe competition or cooperation to the problem at hand. A transform method that greatly simplifies implementation of the compromise solution is presented and … Read more

Newton’s Method for Multiobjective Optimization

We propose an extension of Newton’s Method for unconstrained multiobjective optimization (multicriteria optimization). The method does not scalarize the original vector optimization problem, i.e. we do not make use of any of the classical techniques that transform a multiobjective problem into a family of standard optimization problems. Neither ordering information nor weighting factors for the … Read more