We consider the problem to minimize the sum of piecewise-linear convex functions under both linear and nonnegative constraints. We convert the piecewise-linear convex problem into a standard form linear programming problem (LP) and apply a primal-dual interior-point method for the LP. From the solution of the converted problem, we can obtain the solution of the … Read more
In many telecommunication networks a given set of client nodes must be served by different sets of facilities, providing different services and having different capabilities, which must be located and dimensioned in the design phase. Network topology must be designed as well, by assigning clients to facilities and facilities to higher level entities, when necessary. … Read more
A mathematical programming model for assessing the design of an optimal airport topology is presented herein. It takes into account the efficient and safe taxiing of aircraft on the ground. We balance a set of conflicting factors that depend directly on aircraft trajectories on the ground, such as the number of arriving and departing flights … Read more
Sparse covariance selection problems can be formulated as log-determinant (log-det) semidefinite programming (SDP) problems with large numbers of linear constraints. Standard primal-dual interior-point methods that are based on solving the Schur complement equation would encounter severe computational bottlenecks if they are applied to solve these SDPs. In this paper, we consider a customized inexact primal-dual … Read more
The main concern of this article is to study Ulam stability of the set of $\varepsilon$-approximate minima of a proper lower semicontinuous convex function bounded below on a real normed space $X$, when the objective function is subjected to small perturbations (in the sense of Attouch \& Wets). More precisely, we characterize the class all … Read more
Channel-optimized index assignment of source codewords is arguably the simplest way of improving transmission error resilience, while keeping the source and/or channel codes intact. But optimal design of index assignment is an in- stance of quadratic assignment problem (QAP), one of the hardest optimization problems in the NP-complete class. In this paper we make a … Read more
The number of dual-career couples with children is growing fast. These couples face various challenging problems of organizing their lifes, in particular connected with childcare and time-management. As a typical example we study one of the difficult decision problems of a dual career couple from the point of view of operations research with a particular … Read more
In the paper we consider degree, spectral, and semidefinite bounds on the stability and chromatic numbers of a graph: so-called weak sandwich theorems. We examine the additivity properties of the bounds (the sum of two graphs is their disjoint union), and as an application we tighten the bounds in the weak sandwich theorems, if the … Read more
GRASP with path-relinking (GRASP+PR) is a metaheuristic for finding optimal or near-optimal solutions of combinatorial optimization problems. This paper proposes a new automatic parameter tuning procedure for GRASP+PR heuristics based on a biased random-key genetic algorithm (BRKGA). Given a GRASP+PR heuristic with N input parameters, the tuning procedure makes use of a BRKGA in a … Read more
We propose a new concept of generalized differentiation of set-valued maps that captures the first order information. This concept encompasses the standard notions of Frechet differentiability, strict differentiability, calmness and Lipschitz continuity in single-valued maps, and the Aubin property and Lipschitz continuity in set-valued maps. We present calculus rules, sharpen the relationship between the Aubin … Read more