In this paper, we propose an inexact proximal multiplier method using proximal distances for solving convex minimization problems with a separable structure. The proposed method unified the work of Chen and Teboulle (PCPM method), Kyono and Fukushima (NPCPMM) and Auslender and Teboulle (EPDM) and extends the convergence properties for a class of phi-divergence distances. We … Read more
In multi-objective optimization, one considers optimization problems with more than one objective function, and in general these objectives conflict each other. As the solution set of a multiobjective problem is often rather large and contains points of no interest to the decision-maker, strategies are sought that reduce the size of the solution set. One such … Read more
This paper provides operative point-based formulas (only involving the nominal data, and not data in a neighborhood) for computing or estimating the calmness modulus of the optimal set (argmin) mapping in linear optimization under uniqueness of nominal optimal solutions. Our analysis is developed in two different parametric settings. First, in the framework of canonical perturbations … Read more
The growth-optimal portfolio is designed to have maximum expected log-return over the next rebalancing period. Thus, it can be computed with relative ease by solving a static optimization problem. The growth-optimal portfolio has sparked fascination among finance professionals and researchers because it can be shown to outperform any other portfolio with probability 1 in the … Read more
Enormous global popularity of online social network sites has initiated numerous studies and methods investigating different aspects of their use, so some concepts from network-based studies in optimization theory can be used for research into online networks. In Gaji\’c (2014) are given a several new mixed integer linear programming formulations for first and second problem … Read more
In optimization problems appearing in fields such as economics, finance, or engineering, it is often important that a risk measure of a decision-dependent random variable stays below a prescribed level. At the same time, the underlying probability distribution determining the risk measure’s value is typically known only up to a certain degree and the constraint … Read more
Given a combinatorial optimization problem, we aim at characterizing the set of all instances for which every feasible solution has the same objective value. Our central result deals with multi-dimensional assignment problems. We show that for the axial and for the planar $d$-dimensional assignment problem instances with constant objective value property are characterized by sum-decomposable … Read more
In this paper, we propose a novel, unified, general approach to investigate sufficient and necessary conditions under which four types of convex sets, polyhedra, polyhedral cones, ellipsoids and Lorenz cones, are invariant sets for a linear continuous or discrete dynamical system. In proving invariance of ellipsoids and Lorenz cones for discrete systems, instead of the … Read more
In this paper, we investigate the problem of linear joint probabilistic constraints. We assume that the rows of the constraint matrix are dependent and the dependence is driven by a convenient Archimedean copula. Further we assume the distribution of the constraint rows to be elliptically distributed, covering normal, $t$, or Laplace distributions. Under these and … Read more
We propose the use of controlled perturbations to address the challenging question of optimal active-set prediction for interior point methods. Namely, in the context of linear programming, we consider perturbing the inequality constraints/bounds so as to enlarge the feasible set. We show that if the perturbations are chosen appropriately, the solution of the original problem … Read more