Optimal Magnetic Shield Design with Second-Order Cone Programming

In this paper, we consider a continuous version of the convex network flow problem which involves the integral of the Euclidean norm of the flow and its square in the objective function. A discretized version of this problem can be cast as a second-order cone program, for which efficient primal-dual interior-point algorithms have been developed … Read more

A Conic Programming Approach to Generalized Tchebycheff Inequalities

Consider the problem of finding optimal bounds on the expected value of piece-wise polynomials over all measures with a given set of moments. We show that this problem can be studied within the framework of conic programming. Relying on a key approximation result for conic programming, we show that these bounds can be numerically computed … Read more

A new iteration-complexity bound for the MTY predictor-corrector algorithm

In this paper we present a new iteration-complexity bound for the Mizuno-Todd-Ye predictor-corrector (MTY P-C) primal-dual interior-point algorithm for linear programming. The analysis of the paper is based on the important notion of crossover events introduced by Vavasis and Ye. For a standard form linear program $\min\{c^Tx : Ax=b, \, x \ge 0\}$ with decision … Read more

Using selective orthonormalization to update the analytic center after the addition of multiple cuts

We study the issue of updating the analytic center after multiple cutting planes have been added through the analytic center of the current polytope in Euclidean n-space. This is an important issue that arises at every `stage’ in a cutting plane algorithm. If q cuts are to be added, with q no larger than n, … Read more

A hybrid genetic algorithm for manufacturing cell formation

Cellular manufacturing emerged as a production strategy capable of solving the problems of complexity and long manufacturing lead times in batch production. The fundamental problem in cellular manufacturing is the formation of product families and machine cells. This paper presents a new approach for obtaining machine cells and product families. The approach combines a local … Read more

A Simple Primal-Dual Feasible Interior-Point Methodfor Nonlinear Programming with Monotone Descent

We propose and analyze a primal-dual interior point method of the “feasible” type, with the additional property that the objective function decreases at each iteration. A distinctive feature of the method is the use of different barrier parameter values for each constraint, with the purpose of better steering the constructed sequence away from non-KKT stationary … Read more

The Thirteen Spheres: A New Proof

The “thirteen spheres problem”, also known as the “Gregory-Newton problem” is to determine the maximum number of three-dimensional spheres that can simultaneously touch a given sphere, where all the spheres have the same radius. The history of the problem goes back to a disagreement between Isaac Newton and David Gregory in 1694. Using a combination … Read more

On the superlinear local convergence of a filter-SQP method

Transition to superlinear local convergence is shown for a modified version of the trust-region filter-SQP method for nonlinear programming introduced by Fletcher, Leyffer, and Toint [8]. Hereby, the original trust-region SQP-steps can be used without an additional second order correction. The main modification consists in using the Lagrangian function value instead of the objective function … Read more

”Cone-Free” Primal-Dual Path-Following and Potential Reduction Polynomial Time Interior-Point Methods

We present a framework for designing and analyzing primal-dual interior-point methods for convex optimization. We assume that a self-concordant barrier for the convex domain of interest and the Legendre transformation of the barrier are both available to us. We directly apply the theory and techniques of interior-point methods to the given good formulation of the … Read more