We consider the question of global convergence of iterative methods for nonlinear programming problems. Traditionally, penalty functions have been used to enforce global convergence. In this paper we review a recent alternative, so-called filter methods. Instead of combing the objective and constraint violation into a single function, filter methods view nonlinear optimization as a biobjective … Read more
In the paper, we consider the chance constrained version $$ \Prob\{A_0[x]+\sum_{i=1}^d\zeta_i A_i[x]\succeq0\}\geq1-\epsilon, $$ of an affinely perturbed Linear Matrix Inequality constraint; here $A_i[x]$ are symmetric matrices affinely depending on the decision vector $x$, and $\zeta_1,…,\zeta_d$ are independent of each other random perturbations with light tail distributions (e.g., bounded or Gaussian). Constraints of this type, playing … Read more
The paper is devoted to a revision of the metric regularity property for mappings between metric or Banach spaces. Some new concepts are introduced: uniform metric regularity, metric regularity along a subspace, strong metric regularity for mappings into product spaces, when each component is perturbed independently. Regularity criteria are established based on a nonlocal version … Read more
We consider the problem of identifying multiple outliers in linear regression models. In robust regression the unusual observations should be removed from the sample in order to obtain better fitting for the rest of the observations. Based on the LTS estimate, we propose a penalized trimmed square estimator PTS, where penalty costs for discarding outliers … Read more
Multi-level production planning problems in which multiple items compete for the same resources frequently occur in practice, yet remain daunting in their difficulty to solve. In this paper we propose a heuristic framework that can generate high quality feasible solutions quickly for various kinds of lot-sizing problems. In addition, unlike many other heuristics, it generates … Read more
We discuss in this paper asymptotics of the sample average approximation (SAA) of the optimal value of a minimax stochastic programming problem. The main tool of our analysis is a specific version of the infinite dimensional Delta Method. As an example, we discuss asymptotics of SAA of risk averse stochastic programs involving the absolute semideviation … Read more
This paper is the first of a series of two devoted to the polyhedral study of a strongly NP-hard resource-constrained scheduling problem, referred to as the process move programming problem. This problem arises in relation to the operability of certain high-availability real time distributed systems. After a brief introduction to the problem as well as … Read more
This paper is the second of a series of two devoted to the polyhedral study of a strongly NP-hard resource-constrained scheduling problem, referred to as the process move programming problem. In the present paper, we put back into the picture the capacity constraints which were ignored in the first paper. In doing so, we introduce … Read more
We consider the computational complexity of optimizing various classes of continuous functions over a simplex, hypercube or sphere. These relatively simple optimization problems have many applications. We review known approximation results as well as negative (inapproximability) results from the recent literature. CitationCentER Discussion paper 2006-85 Tilburg University THe NetherlandsArticleDownload View PDF
We consider k-regular graphs with loops, and study the Lovász theta-numbers and Schrijver theta’-numbers of the graphs that result when the loop edges are removed. We show that the theta-number dominates a recent eigenvalue upper bound on the stability number due to Godsil and Newman [C.D. Godsil and M.W. Newman. Eigenvalue bounds for independent sets. … Read more