We study a steered sequential gradient algorithm which minimizes the sum of convex functions by proceeding cyclically in the directions of the negative gradients of the functions and using steered step-sizes. This algorithm is applied to the convex feasibility problem by minimizing a proximity function which measures the sum of the Bregman distances to the … Read more
One of the main issues in the glass industry is the minimization of the trim loss generated when cutting large parts (stocks) into small items. In our application stocks are produced in the plant. Many distinct stock sizes are feasible, and technical constraints limit the variety of cutting patterns to those producing a single type … Read more
We discuss computational enhancements for the low-rank semidefinite programming algorithm, including the extension to block semidefinite programs, an exact linesearch procedure, and a dynamic rank reduction scheme. A truncated Newton method is also introduced, and several preconditioning strategies are proposed. Numerical experiments illustrating these enhancements are provided. Citation Manuscript, Department of Mangagement Sciences, University of … Read more
We examine the problem of approximating, in the Frobenius-norm sense, a positive, semidefinite symmetric matrix by a rank-one matrix, with an upper bound on the cardinality of its eigenvector. The problem arises in the decomposition of a covariance matrix into sparse factors, and has wide applications ranging from biology to finance. We use a modification … Read more
Seismic reflection tomography is a method for determining a subsurface velocity model from the traveltimes of seismic waves reflecting on geological interfaces. From an optimization viewpoint, the problem consists in minimizing a nonlinear least-squares function measuring the mismatch between observed traveltimes and those calculated by ray tracing in this model. The introduction of a priori … Read more
In this paper we present a methodology to decide capacity expansions for a transit network that finds a robust solution with respect to the uncertainty in demands and travel times. We show that solving for a robust solution is a computationally tractable problem under conditions that are reasonable for a transportation system. For example, the … Read more
A new method for data-based fuzzy system modeling is presented. The approach uses Takagi-Sugeno models and Adaptive Simulated Annealing (ASA) to achieve its goal . The problem to solve is well defined – given a training set containing a finite number of input-output pairs, construct a fuzzy system that approximates the behavior of the real … Read more
We deal with the problem of scheduling preventive maintenance (PM) by minimizing a performance function which reflects repair and replacement costs as well as the costs of the PM itself. It is assumed that there is a known model which predicts the frequency of system failure as a function of its age; and it is … Read more
We consider two notions for the representations of convex cones: $G$-representation and lifted-$G$-representation. The former represents a convex cone as a slice of another; the latter allows in addition, the usage of auxiliary variables in the representation. We first study the basic properties of these representations. We show that some basic properties of convex cones … Read more
The vast size of real world stochastic programming instances requires sampling to make them practically solvable. In this paper we extend the understanding of how sampling affects the solution quality of multistage stochastic programming problems. We present a new heuristic for determining good feasible solutions for a multistage decision problem. For power and log-utility functions … Read more