Parallel interior-point solver for structured linear programs
Abstract. Issues of implementation of an object-oriented library for parallel interior-point methods are addressed. The solver can easily exploit any special structure of the underlying optimization...
View ArticlePreconditioning Indefinite Systems in Interior Point Methods for Optimization
AbstractEvery Newton step in an interior-point method for optimization requires a solution of a symmetric indefinite system of linear equations. Most of today's codes apply direct solution methods to...
View ArticleAn Interior Point Heuristic for the Hamiltonian Cycle Problem via Markov...
AbstractWe consider the Hamiltonian cycle problem embedded in a singularly perturbed Markov decision process (MDP). More specifically, we consider the HCP as an optimization problem over the space of...
View ArticleDirect Solution of Linear Systems of Size 10 9 Arising in Optimization with...
AbstractSolution methods for very large scale optimization problems are addressed in this paper. Interior point methods are demonstrated to provide unequalled efficiency in this context. They need a...
View ArticleInexact constraint preconditioners for linear systems arising in interior...
Abstract Issues of indefinite preconditioning of reduced Newton systems arising in optimization with interior point methods are addressed in this paper. Constraint preconditioners have shown much...
View ArticleParallel interior-point solver for structured quadratic programs: Application...
AbstractMany practical large-scale optimization problems are not only sparse, but also display some form of block-structure such as primal or dual block angular structure. Often these structures are...
View ArticleFurther development of multiple centrality correctors for interior point methods
Abstract This paper addresses the role of centrality in the implementation of interior point methods. We provide theoretical arguments to justify the use of a symmetric neighbourhood, and translate...
View ArticleHigh-Performance Parallel Support Vector Machine Training
AbstractSupport vector machines are a powerful machine learning technology, but the training process involves a dense quadratic optimization problem and is computationally expensive. We show how the...
View ArticleA Structure Conveying Parallelizable Modeling Language for Mathematical...
Modeling languages are an important tool for the formulation of mathematical programming problems. Many real-life mathematical programming problems are of sizes that make their solution by parallel...
View ArticleExploiting structure in parallel implementation of interior point methods for...
AbstractOOPS is an object-oriented parallel solver using the primal–dual interior point methods. Its main component is an object-oriented linear algebra library designed to exploit nested block...
View ArticleA structure-conveying modelling language for mathematical and stochastic...
AbstractWe present a structure-conveying algebraic modelling language for mathematical programming. The proposed language extends AMPL with object-oriented features that allows the user to construct...
View ArticleA warm-start approach for large-scale stochastic linear programs
AbstractWe describe a way of generating a warm-start point for interior point methods in the context of stochastic programming. Our approach exploits the structural information of the stochastic...
View ArticleExploiting separability in large-scale linear support vector machine training
AbstractLinear support vector machine training can be represented as a large quadratic program. We present an efficient and numerically stable algorithm for this problem using interior point methods,...
View ArticleGPU Acceleration of the Matrix-Free Interior Point Method
AbstractThe matrix-free technique is an iterative approach to interior point methods (IPM), so named because both the solution procedure and the computation of an appropriate preconditioner require...
View ArticleMatrix-free interior point method
AbstractIn this paper we present a redesign of a linear algebra kernel of an interior point method to avoid the explicit use of problem matrices. The only access to the original problem data needed are...
View ArticleMatrix-free interior point method for compressed sensing problems
AbstractWe consider a class of optimization problems for sparse signal reconstruction which arise in the field of compressed sensing (CS). A plethora of approaches and solvers exist for such problems,...
View ArticleA second-order method for strongly convex $$\ell _1$$ ℓ 1 -regularization...
AbstractIn this paper a robust second-order method is developed for the solution of strongly convex \(\ell _1\)-regularized problems. The main aim is to make the proposed method as inexpensive as...
View ArticleA new warmstarting strategy for the primal-dual column generation method
AbstractThis paper presents a new warmstarting technique in the context of a primal-dual column generation method applied to solve a particular class of combinatorial optimization problems. The...
View ArticleLarge-scale optimization with the primal-dual column generation method
AbstractThe primal-dual column generation method (PDCGM) is a general-purpose column generation technique that relies on the primal-dual interior point method to solve the restricted master problems....
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