Robust Solutions of MultiObjective Linear Semi-Infinite Programs under Constraint Data Uncertainty

Abstract

Abstract. The multi-objective optimization model studied in this paper deals with simultaneous minimization of finitely many linear functions subject to an arbitrary number of uncertain linear constraints. We first provide a radius of robust feasibility guaranteeing the feasibility of the robust counterpart under affine data parametrization. We then establish dual characterizations of robust solutions of our model that are immunized against data uncertainty by way of characterizing corresponding solutions of robust counterpart of the model. Consequently we present robust duality theorems relating the value of the robust model with the corresponding value of its dual problem.

A comparative note on the relaxation algorithms for the linear semi-infinite feasibility problem

“…From (23), combinations of L-matrices can be built incrementally, by taking initially the first n + 1 support vectors (which yields the unique combination L = {l 1 , l 2 , . .…”

“…In particular, the feasibility of a robust linear optimization problem can be reformulated as an example of (LF P ) [13]. For more recent development for robust linear multi-objective optimization problem see [23] and [24]. Observe also that any convex (possibly semi-infinite) feasibility problem Find x ∈ R n such that g s (x) ≤ 0, ∀s ∈ S, can be linearized in different ways (e.g., as in [25, (7.10)] or [19, pp.…”

Robust solutions to multi-objective linear programs with uncertain data

“…We finally note that in the case when the objective function is free of uncertainty, the characterization of a robust solution for uncertain multi-objective linear programming problem under ellipsoidal constraint data uncertainty was derived in Goberna et al (2014).…”

“…Particular types of uncertain multi-objective linear programming problems have already been studied, e.g., Sitarz (2008) considers changes in one objective function via sensitivity analysis, while Pando, Luc, and Pardalos (2013) consider changes in the whole objective function x → Cx and Goberna, Jeyakumar, Li, and Vicente-Pérez (2014) considers change in the constraints by using different robustness approaches. The purpose of the present work is to study multiobjective linear programming problems in the face of data uncertainty both in the objective function and constraints from a robustness perspective.…”

Radius of robust feasibility formulas for classes of convex programs with uncertain polynomial constraints

“…In this case, the proof of Theorem 2.1 leads to a simple formula for the radius of robust feasibility of uncertain linear program, derived in [12,13]…”