We study the maximum flow problem subject to binary disjunctive constraints in a directed graph: A negative disjunctive constraint states that a certain pair of arcs in a digraph cannot be simultaneously used for sending flow in a feasible solution. In contrast to this, positive disjunctive constraints force that for certain pairs of arcs at … Read more
Uncertain programs have been developed to deal with optimization problems including inexact data, i.e., uncertainty. A deterministic approach called robust optimization is commonly applied to solve these problems. Recently, Calafiore and Campi have proposed a randomized approach based on sampling of constraints, where the number of samples is determined so that only small portion of … Read more
We consider wireless telecommunications systems with orthogonal frequency bands, where each band is referred to as a channel, e.g., orthogonal frequencydivision multiple access (OFDMA). For a snap-shot in time, a joint channel assignment and power allocation optimization problem is presented, both in downlink and in uplink, where the objective is to maximize the minimum total … Read more
We present three new copositivity tests based upon difference-of-convex (d.c.) decompositions, and combine them to a branch-and-bound algorithm of $\omega$-subdivision type. The tests employ LP or convex QP techniques, but also can be used heuristically using appropriate test points. We also discuss the selection of efficient d.c.~decompositions and propose some preprocessing ideas based on the … Read more
We show that the Laplace approximation of a supremum by $L^p$-norms has interesting consequences in optimization. For instance, the logarithmic barrier functions (LBF) of a primal convex problem $P$ and its dual $P^*$ appear naturally when using this simple approximation technique for the value function $g$ of $P$ or its Legendre-Fenchel conjugate $g^*$. In addition, … Read more
Given a compact parameter set $Y\subset R^p$, we consider polynomial optimization problems $(P_\y$) on $R^n$ whose description depends on the parameter $y\in Y$. We assume that one can compute all moments of some probability measure $\varphi$ on $Y$, absolutely continuous with respect to the Lebesgue measure (e.g. $Y$ is a box or a simplex and … Read more
We consider sequential quadratic programming (SQP) methods for solving constrained nonlinear programming problems. It is generally believed that SQP methods are sensitive to the accuracy by which partial derivatives are provided. One reason is that differences of gradients of the Lagrangian function are used for updating a quasi-Newton matrix, e.g., by the BFGS formula. The … Read more
This paper studies stability of error bounds for convex constraint systems in Banach spaces. We show that certain known sufficient conditions for local and global error bounds actually ensure error bounds for the family of functions being in a sense small perturbations of the given one. A single inequality as well as semi-infinite constraint systems … Read more
Total variation (TV) regularization is popular in image restoration and reconstruction due to its ability to preserve image edges. To date, most research activities on TV models concentrate on image restoration from blurry and noisy observations, while discussions on image reconstruction from random projections are relatively fewer. In this paper, we propose, analyze, and test … Read more
In this paper we develop efficient heuristic algorithms to solve the bottleneck traveling salesman problem (BTSP). Results of extensive computational experiments are reported. Our heuristics produced optimal solutions for all the test problems considered from TSPLIB, JM-instances, National TSP instances, and VLSI TSP instances in very reasonable running time. We also conducted experiments with specially … Read more