In cutting plane methods, the question of how to generate the “best possible” set of cuts is both central and crucial. We propose a lexicographic multi-objective cutting plane generation scheme that generates, among all the maximally violated valid inequalities of a given family, an inequality that is undominated and maximally diverse w.r.t. the cuts that … Read more
In this work, we propose an inexact projected gradient-like method for solving smooth constrained vector optimization problems. In the unconstrained case, we retrieve the steepest descent method introduced by Graña Drummond and Svaiter. In the constrained setting, the method we present extends the exact one proposed by Graña Drummond and Iusem, since it admits relative … Read more
In this paper, firstly, a generalized subconvexlike set-valued map involving the relative algebraic interior is introduced in ordered linear spaces. Secondly, some properties of a generalized subconvexlike set-valued map are investigated. Finally, the optimality conditions of set-valued optimization problem are established. Citation {\bf AMS 2010 Subject Classifications:} 90C26, 90C29, 90C30ArticleDownload View PDF
The use of metaheuristics in Multi-objective Combinatorial Optimization, particularly Ant Colony Optimization (ACO), has grown recently. This paper proposes an approach where multi-species ants compete for food resources. Each species has its own search strategy and do not access pheromone information of other species. As in nature, successful ant populations are allowed to grow, whereas … Read more
Stochastic dominance theory provides tools to compare random entities. When comparing random vectors (say X and Y ), the problem can be viewed as one of multi-criterion decision making under uncertainty. One approach is to compare weighted sums of the components of these random vectors using univariate dominance. In this paper we propose new concepts … Read more
We consider the problem of approximating the Pareto set of convex multi-criteria optimization problems by a discrete set of points and their convex combinations. Finding the scalarization parameters that maximize the improvement in bound on the approximation error when generating a single Pareto optimal solution is a nonconvex optimization problem. This problem is solvable by … Read more
In this paper new results are established in multiobjective DC programming with infinite convex constraints ($MOPIC$ for abbr.) that are defined on Banach space (finite or infinite) with objectives given as the difference of convex functions subject to infinite convex constraints. This problem can also be called multiobjective DC semi-infinite and infinite programming, where decision … Read more
We present explicit optimality conditions for a nonsmooth functional defined over the (properly or weakly) Pareto set associated to a multiobjective linear-quadratic control problem. This problem is very difficult even in a finite dimensional setting, i.e. when, instead of a control problem, we deal with a mathematical programming problem. Amongst different applications, our problem may … Read more
In this paper we introduce robust and stochastically weighted sum approaches to deterministic and stochastic multi-objective optimization. The robust weighted sum approach minimizes the worst case weighted sum of objectives over a given weight region. We study the reformulations of the robust weighted sum problem under different definitions of deterministic weight regions. We next introduce … Read more
We present a new approach to the study of a set-valued equilibrium problem (for short, SEP) through the study of a set-valued optimization problem with a geometric constraint (for short, SOP) based on an equivalence between solutions of these problems. As illustrations, we adapt to SEP enhanced notions of relative Pareto efficient solutions introduced in … Read more