Výsledky vyhledávání - "Jacek Gondzio"

A New Stopping Criterion for Krylov Solvers Applied in Interior Point Methods

Publikováno v: SIAM Journal on Scientific Computing. 45:A703-A728

When an iterative method is applied to solve the linear equation system in interior point methods (IPMs), the attention is usually placed on accelerating their convergence by designing appropriate preconditioners, but the linear solver is applied as

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::896510c6be54704eabaa50b9365f74f2
https://doi.org/10.1137/22m1490041

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Proximal Stabilized Interior Point Methods and Low-Frequency-Update Preconditioning Techniques

Autor: Stefano Cipolla, Jacek Gondzio

Publikováno v: Journal of Optimization Theory and Applications. 197:1061-1103

In this work, in the context of Linear and convex Quadratic Programming, we consider Primal Dual Regularized Interior Point Methods (PDR-IPMs) in the framework of the Proximal Point Method. The resulting Proximal Stabilized IPM (PS-IPM) is strongly s

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::54cbfee1401d6f30f9752f27053f75e7
https://doi.org/10.1007/s10957-023-02194-4

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General-purpose preconditioning for regularized interior point methods

Autor: Jacek Gondzio, Spyridon Pougkakiotis, John W. Pearson

Publikováno v: Computational Optimization and Applications. 83:727-757

In this paper we present general-purpose preconditioners for regularized augmented systems, and their corresponding normal equations, arising from optimization problems. We discuss positive definite preconditioners, suitable for CG and MINRES. We con

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::16132ea6e033a210b510ce20b690d011
https://doi.org/10.1007/s10589-022-00424-5

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An Interior Point–Inspired Algorithm for Linear Programs Arising in Discrete Optimal Transport

Autor: Filippo Zanetti, Jacek Gondzio

Publikováno v: INFORMS Journal on Computing.

Discrete optimal transport problems give rise to very large linear programs (LPs) with a particular structure of the constraint matrix. In this paper, we present a hybrid algorithm that mixes an interior point method (IPM) and column generation, spec

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https://doi.org/10.1287/ijoc.2022.0184

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New algorithms for hierarchical optimisation in kidney exchange programmes

Autor: Maxence Delorme, Sergio García, Jacek Gondzio, Jörg Kalcsics, David Manlove, William Pettersson

Publikováno v: Operations Research. INFORMS Inst.for Operations Res.and the Management Sciences

Kidney exchange programmes (KEPs) across the world help match donors and recipients to identify kidney transplantations. Almost all KEPs use a hierarchical set of objectives to determine an optimal set of transplants to perform, and integer linear pr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f3e00f942a2f81616f9ed0f34280f4cc
https://research.tilburguniversity.edu/en/publications/35197bbb-1cba-49b2-b977-ce24e3be8401

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An Interior Point-Proximal Method of Multipliers for Linear Positive Semi-Definite Programming

Autor: Spyridon Pougkakiotis, Jacek Gondzio

Publikováno v: Journal of Optimization Theory and Applications. 192:97-129

In this paper we generalize the Interior Point-Proximal Method of Multipliers (IP-PMM) presented in Pougkakiotis and Gondzio (Comput Optim Appl 78:307–351, 2021.10.1007/s10589-020-00240-9) for the solution of linear positive Semi-Definite Programmi

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https://doi.org/10.1007/s10957-021-01954-4

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Global solutions of nonconvex standard quadratic programs via mixed integer linear programming reformulations

Autor: Jacek Gondzio, E. Alper Yıldırım

Publikováno v: Journal of Global Optimization. 81:293-321

A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We propose t

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https://doi.org/10.1007/s10898-021-01017-y

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Rank revealing Gaussian elimination by the maximum volume concept

Autor: Lukas Schork, Jacek Gondzio

Publikováno v: Schork, L & Gondzio, J 2020, ' Rank revealing Gaussian elimination by the maximum volume concept ', Linear algebra and its applications . https://doi.org/10.1016/j.laa.2019.12.037

A Gaussian elimination algorithm is presented that reveals the numerical rank ofa matrix by yielding small entries in the Schur complement. The algorithm uses the maximum volume concept to nd a square nonsingular submatrix of maximum dimension. The b

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::11320a938c5e90aca708c7f752a4b2e6
https://doi.org/10.1016/j.laa.2019.12.037

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Implementation of an interior point method with basis preconditioning

Autor: Lukas Schork, Jacek Gondzio

Publikováno v: Schork, L & Gondzio, J 2020, ' Implementation of an Interior Point Method with Basis Preconditioning ', Mathematical Programming Computation, vol. 12, pp. 603–635 . https://doi.org/10.1007/s12532-020-00181-8

The implementation of a linear programming interior point solver is described that is based on iterative linear algebra. The linear systems are preconditioned by a basis matrix, which is updated from one interior point iteration to the next to bound

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::54ea81f18ddc742360d231645b25e1f3
https://doi.org/10.1007/s12532-020-00181-8

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Fast Solution Methods for Convex Quadratic Optimization of Fractional Differential Equations

Autor: Spyridon Pougkakiotis, Jacek Gondzio, John W. Pearson, Santolo Leveque

Publikováno v: Pougkakiotis, S, Pearson, J W, Leveque, S & Gondzio, J 2020, ' FAST SOLUTION METHODS FOR CONVEX QUADRATIC OPTIMIZATION OF FRACTIONAL DIFFERENTIAL EQUATIONS ', SIAM Journal on Matrix Analysis and Applications, vol. 41, no. 3, pp. 1443–1476 . https://doi.org/10.1137/19M128288X

In this paper, we present numerical methods suitable for solving convex quadratic Fractional Differential Equation (FDE) constrained optimization problems, with box constraints on the state and/or control variables. We develop an Alternating Directio

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d58e9696584f9061fbb0ca25c4b1833f
https://doi.org/10.1137/19m128288x

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