Jordan-algebraic aspects of nonconvex optimization over symmetric cones

被引：27

作者：

Faybusovich, L ^{[1
]}

Lu, Y ^{[1
]}

机构：

[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2006年 / 53卷 / 01期

关键词：

Jordan algebras; symmetric cone; nonconvex optimization;

D O I：

10.1007/s00245-005-0835-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We illustrate the usefulness of Jordan-algebraic techniques for non-convex optimization by considering a potential-reduction algorithm for a non-convex quadratic function over the domain obtained as the intersection of a symmetric cone with an affine subspace.

引用

页码：67 / 77

页数：11

共 13 条

[1]

Bonnans JF., 2013, PERTURBATION ANAL OP

[2]

Faraut J., 1994, Analysis on symmetric cones

[3] Linear systems in Jordan algebras and primal-dual interior-point algorithms [J].

Faybusovich, L .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1997, 86 (01) :149-175

[4] A Jordan-algebraic approach to potential-reduction algorithms [J].

Faybusovich, L .

MATHEMATISCHE ZEITSCHRIFT, 2002, 239 (01) :117-129

[5] Primal-dual algorithms and infinite-dimensional Jordan algebras of finite rank [J].

Faybusovich, L ;

Tsuchiya, T .

MATHEMATICAL PROGRAMMING, 2003, 97 (03) :471-493

[6] Euclidean Jordan algebras and interior-point algorithms [J].

Faybusovich, L .

POSITIVITY, 1997, 1 (04) :331-357

[7] A long-step primal-dual algorithm for the symmetric programming problem [J].

Faybusovich, L ;

Arana, R .

SYSTEMS & CONTROL LETTERS, 2001, 43 (01) :3-7

[8] On a commutative class of search directions for linear programming over symmetric cones [J].

Muramatsu, M .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2002, 112 (03) :595-625

[9]

Renegar J, 2001, SER MPSSIAM SERIES O

[10] Extension of primal-dual interior point algorithms to symmetric cones [J].

Schmieta, SH ;

Alizadeh, F .

MATHEMATICAL PROGRAMMING, 2003, 96 (03) :409-438

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