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
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
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
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
Chemotherapy operations planning and scheduling in oncology clinics is a complex problem due to several factors such as the cyclic nature of chemotherapy treatment plans, the high variability in resource requirements (treatment time, nurse time, pharmacy time) and the multiple clinic resources involved. Treatment plans are made by oncologists for each patient according to existing … Read more
The class of sufficient matrices is important in the study of the linear complementarity problem(LCP) – some interior point methods (IPM’s) for LCP’s with sufficient data matrices have complexity polynomial in the bit size of the matrix and its handicap. In this paper we show that the handicap of a sufficient matrix may be exponential … Read more
In this paper we deal with the Critical Node Problem (CNP), i.e., the problem of searching for a given number K of nodes in a graph G, whose removal minimizes the number of connections between pairs of nodes in the residual graph. While the NP-completeness of this problem for general graphs has been already established … Read more
For a semialgebraic set K in R^n, let P_d(K) be the cone of polynomials in R^n of degrees at most d that are nonnegative on K. This paper studies the geometry of its boundary. When K=R^n and d is even, we show that its boundary lies on the irreducible hypersurface defined by the discriminant of … Read more
In this paper, we compare the performance of two scenario-based numerical methods to solve stochastic optimal control problems: scenario trees and particles. The problem consists in finding strategies to control a dynamical system perturbed by exogenous noises so as to minimize some expected cost along a discrete and finite time horizon. We introduce the Mean … Read more
This paper considers a portfolio selection problem in which portfolios with minimum number of active assets are sought. This problem is motivated by the need of inducing sparsity on the selected portfolio to reduce transaction costs, complexity of portfolio management, and instability of the solution. The resulting problem is a difficult combinatorial problem. We propose … Read more