Robust optimization extends stochastic programming models by incorporating measures of variability into the objective function. This paper explores robust optimization in the context of two-stage planning systems. First, we propose the use of a generalized Benders decomposition algorithm for solving robust models. Next, we argue that using an arbitrary measure for variability can lead to … Read more
This paper demonstrates that for generalized methods of multipliers for convex programming based on Bregman distance kernels — including the classical quadratic method of multipliers — the minimization of the augmented Lagrangian can be truncated using a simple, generally implementable stopping criterion based only on the norms of the primal iterate and the gradient (or … Read more
We discuss convex optimization problems where some of the variables are constrained to be finite autocorrelation sequences. Problems of this form arise in signal processing and communications, and we describe applications in filter design and system identification. Autocorrelation constraints in optimization problems are often approximated by sampling the corresponding power spectral density, which results in … Read more
We consider convex optimization problems with the constraint that the variables form a finite autocorrelation sequence, or equivalently, that the corresponding power spectral density is nonnegative. This constraint is often approximated by sampling the power spectral density, which results in a set of linear inequalities. It can also be cast as a linear matrix inequality … Read more
In this article, we are interested in the minimization of functionals in the set of convex functions. We investigate the discretization of the convexity through various numerical methods and find a geometrical obstruction confirmed by numerical simulations. We prove that there exist some convex functions that cannot be the limit of any conformal $P_1$ Finite … 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
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
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. Article Download View Generating Convex … Read more
Conic quadratic optimization is the problem of minimizing a linear function subject to the intersection of an affine set and the product of quadratic cones. The problem is a convex optimization problem and has numerous applications in engineering, economics, and other areas of science. Indeed, linear and convex quadratic optimization is a special case. Conic … Read more