Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. SIAM J. OPTIM. c  2014 Society for Industrial and Applied Mathematics Vol. 24, No. 3, pp. 1402–1419 ROBUST SOLUTIONS OF MULTIOBJECTIVE LINEAR SEMI-INFINITE PROGRAMS UNDER CONSTRAINT DATA UNCERTAINTY ∗ M. A. GOBERNA † , V. JEYAKUMAR ‡ , G. LI ‡ , AND J. VICENTE-P ´ EREZ ‡ Abstract. The multiobjective optimization model studied in this paper deals with simulta- neous 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. Key words. linear semi-infinite programming, linear multiobjective optimization, robust opti- mization, duality AMS subject classifications. 90C29, 90C31, 90C34 DOI. 10.1137/130939596 1. Introduction. Consider the deterministic multiobjective linear semi-infinite program of the form (1.1) (P ) V-min x∈R n ( c ⊤ 1 x,...,c ⊤ m x ) such that (s.t.) a ⊤ t x ≥ b t ∀t ∈ T, where V-min stands for vector minimization, c i ∈ R n for all i ∈ I := {1,...,m}, the superscript ⊤ denotes transpose, (a t ,b t ) ∈ R n × R for all t ∈ T , and the index set T is arbitrary. When T is finite, (P ) becomes an ordinary multiobjective linear optimization problem, whereas, when T is infinite, (P ) is a multiobjective linear semi- infinite optimization problem. Some potential applications of these models have been discussed in [9]. In particular, whenever m = 1, (P ) becomes a single-objective linear semi-infinite program which has been extensively studied in the literature (see [8, 13] and other references therein). When dealing with real-world optimization problems, the input data associated with a multiobjective linear semi-infinite program are often noisy or uncertain due to prediction or measurement errors. For example, a multiobjective optimization problem arising in industry or commerce might involve various costs, financial returns, and future demands that might be unknown at the time of the decision. They have to be predicted and are replaced with their forecasts. They often result in prediction errors. Similarly, some of the data, such as the contents associated with raw materials, might be hard to measure exactly. These input data are subject to measurement errors. ∗ Received by the editors October 2, 2013; accepted for publication (in revised form) May 15, 2014; published electronically August 19, 2014. This research was partially supported by the Australian Research Council, Discovery Project DP120100467, the MICINN of Spain, grant MTM2011-29064- C03-02, and Generalitat Valenciana, grant ACOMP/2013/062. http://www.siam.org/journals/siopt/24-3/93959.html † Department of Statistics and Operations Research, University of Alicante, 03080 Alicante, Spain (mgoberna@ua.es). ‡ Department of Applied Mathematics, University of New South Wales, Sydney 2052, Australia (v.jeyakumar@unsw.edu.au, g.li@unsw.edu.au, jose.vicente@ua.es). 1402