In this paper we address a general Goal Programming problem with linear objectives, convex constraints, and an arbitrary componentwise nondecreasing norm to aggregate deviations with respect to targets. In particular, classical Linear Goal Programming problems, as well as several models in Location and Regression Analysis are modeled within this framework. In spite of its generality, … Read more
A greedy randomized adaptive search procedure (GRASP) is a metaheuristic for combinatorial optimization. It is a multi-start or iterative process, in which each {GRASP} iteration consists of two phases, a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed … Read more
In this work we summarize the basic elements of primal and dual Newton algorithms for network optimization with continuously differentiable (strictly) convex arc cost functions. Both the basic mathematics and implementation are discussed, and hints to important tuning details are made. The exposition assumes that the reader posseses a significant level of prior knowledge in … Read more
This paper surveys frequency assignment problems coming up in planning wireless communication services. It particularly focuses on cellular mobile phone systems such as GSM, a technology that revolutionizes communication. Traditional vertex coloring provides a conceptual framework for the mathematical modeling of many frequency planning problems. This basic form, however, needs various extensions to cover technical … Read more
In this paper we describe the results of a computational study towards the (re)optimization of signaling transfer points (STPs) in telecommunication networks. The best performance of an STP is achieved whenever the traffic load is evenly distributed among the internal components. Due to the continuously changing traffic pattern, the load of the components has to … Read more
We study two issues on condition numbers for convex programs: one has to do with the growth of the condition numbers of the linear equations arising in interior-point algorithms; the other deals with solving conic systems and estimating their distance to infeasibility. These two issues share a common ground: the key tool for their development … Read more
We develop a method for generating valid convex polynomial inequalities for mixed 0-1 convex programs. We also show how these inequalities can be generated in the linear case by defining cut generation problems using a projection cone. The basic results for quadratic inequalities are extended to generate convex polynomial inequalities. ArticleDownload View PDF
Let $S\subset[-1,1)$. A finite set $C=\{x_i\}_{i=1}^M\subset\Re^n$ is called a {\em spherical S-code} if $||x_i||=1$ for each $i$, and $x_i^T x_j\in S$, $i\ne j$. For $S=[-1,.5]$ maximizing $M=|C|$ is commonly referred to as the {\em kissing number} problem. A well-known technique based on harmonic analysis and linear programming can be used to bound $M$. We consider … Read more
In the vicinity of a solution of a nonlinear programming problem at which both strict complementarity and linear independence of the active constraints may fail to hold, we describe a technique for distinguishing weakly active from strongly active constraints. We show that this information can be used to modify the sequential quadratic programming algorithm so … Read more
Slice models are collections of mathematical programs with the same structure but different data. Examples of slice models appear in Data Envelopment Analysis, where they are used to evaluate efficiency, and cross-validation, where they are used to measure generalization ability. Because they involve multiple programs, slice models tend to be data-intensive and time consuming to … Read more