In this paper, we propose an interior-point method for large sparse minimax optimization. After a short introduction, where various barrier terms are discussed, the complete algorithm is introduced and some implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Thus nonconvex problems can be solved successfully. The results … Read more
In this paper, we propose an interior-point method for large sparse l_1 optimization. After a short introduction, the complete algorithm is introduced and some implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Thus nonconvex problems can be solved successfully. The results of computational experiments given in this … Read more
In this paper, we investigate the use of an exact primal-dual penalty approach within the framework of an interior-point method for nonconvex nonlinear programming. This approach provides regularization and relaxation, which can aid in solving ill-behaved problems and in warmstarting the algorithm. We present details of our implementation within the LOQO algorithm and provide extensive … Read more
This papers describes a perl language program to create time-to-target solution value plots for measured CPU times that are assumed to fit a shifted exponential distribution. This is often the case in local search based heuristics for combinatorial optimization, such as simulated annealing, genetic algorithms, iterated local search, tabu search, WalkSAT, and GRASP. Such plots … Read more
In this paper we develop a practical primal interior decomposition algorithm for two-stage stochastic programming problems. The framework of this algorithm is similar to the framework in Mehrotra and \”{Ozevin} \cite{MO04a,MO04b} and Zhao \cite{GZ01}, however their algorithm is altered in a simple yet fundamental way to achieve practical performance. In particular, this new algorithm weighs … Read more
We consider the problem of interconnecting a set of customer sites using SONET rings of equal capacity, which can be defined as follows: Given an undirected graph G=(V,E) with nonnegative edge weight d(u,v), (u,v) in E, and two integers K and B, find a partition of the nodes of G into K subsets so that … Read more
We present the Sequential Subspace Optimization (SESOP) method for large scale smooth unconstrained problems. At each iteration we search for a minimum of the objective function over a subspace spanned by the current gradient and by directions of few previous steps. We also include into this subspace the direction from the starting point to the … Read more
Given r real functions F1 (x), . . . , Fr (x) and an integer p between 1 and r, the Low Order- Value Optimization problem (LOVO) consists of minimizing the sum of the functions that take the p smaller values. If (y1 , . . . , yr ) is a vector of data … Read more
This paper addresses the role of centrality in the implementation of interior point methods. Theoretical arguments are provided to justify the use of a symmetric neighbourhood. These are translated into computational practice leading to a new insight into the role of re-centering in the implementation of interior point methods. Arguments are provided to show that … Read more
Piecewise linear functions (PLFs) are commonly used to approximate nonlinear functions. They are also of interest in their own, arising for example in problems with economies of scale. Early approaches to piecewise linear optimization (PLO) assumed continuous PLFs. They include the incremental cost MIP model of Markowitz and Manne and the convex combination MIP model … Read more