Computing Conjugate Barrier Information for Nonsymmetric Cones

被引：2

作者：

Kapelevich, Lea ^{[1
]}

Andersen, Erling D. ^{[2
]}

Vielma, Juan Pablo ^{[3
,4
]}

机构：

[1] MIT, Operat Res Ctr, 77 Massachusetts Ave, Cambridge, MA 02139 USA

[2] MOSEK ApS, Copenhagen, Denmark

[3] Google Res, Cambridge, MA USA

[4] MIT Sloan Sch Management, Cambridge, MA USA

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2024年 / 202卷 / 01期

基金：

美国国家科学基金会;

关键词：

Conjugate barrier function; Nonsymmetric cones; Interior point; INTERIOR-POINT METHODS;

D O I：

10.1007/s10957-022-02076-1

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

The recent interior point algorithm by Dahl and Andersen [10] for nonsymmetric cones as well as earlier works [18, 21] require derivative information from the conjugate of the barrier function of the cones in the problem. Besides a few special cases, there is no indication of when this information is efficient to evaluate. We show how to compute the gradient of the conjugate barrier function for seven useful nonsymmetric cones. In some cases, this is helpful for deriving closed-form expressions for the inverse Hessian operator for the primal barrier.

引用

页码：271 / 295

页数：25

共 31 条

[1] Logarithmic barriers for sparse matrix cones
Andersen, Martin S.
Dahl, Joachim
Vandenberghe, Lieven
[J]. OPTIMIZATION METHODS & SOFTWARE, 2013, 28 (03) : 396 - 423
[2] CSDP, a C library for semidefinite programming
Borchers, B
[J]. OPTIMIZATION METHODS & SOFTWARE, 1999, 11-2 (1-4) : 613 - 623
[3] Chares R., 2009, Ph.D. thesis
[4] Coey C., ARXIV
[5] Coey C., 2021, ARXIV
[6] Coey C., THESIS MIT
[7] Coey C., 2021, HYPATIA CONES REFERE
[8] Solving Natural Conic Formulations with Hypatia.jl
Coey, Chris
Kapelevich, Lea
Vielma, Juan Pablo
[J]. INFORMS JOURNAL ON COMPUTING, 2022, 34 (05) : 2686 - 2699
[9] Corless R. M., 2002, Artificial Intelligence, Automated Reasoning, and Symbolic Computation. Joint International Conferences AISC 2002 and Calculemus 2002. Proceedings (Lecture Notes in Computer Science Vol.2385), P76
[10] A primal-dual interior-point algorithm for nonsymmetric exponential-cone optimization
Dahl, Joachim
Andersen, Erling D.
[J]. MATHEMATICAL PROGRAMMING, 2022, 194 (1-2) : 341 - 370

← 1 2 3 4 →