Extension of primal-dual interior point methods to diff-convex problems on symmetric cones

被引：3

作者：

Valkonen, Tuomo ^{[1
,2
]}

机构：

[1] Univ Jyvaskyla, Dept Math Informat Technol, SF-40351 Jyvaskyla, Finland

[2] Karl Franzens Univ Graz, Inst Math & Sci Comp, Graz, Austria

来源：

OPTIMIZATION | 2013年 / 62卷 / 03期

关键词：

symmetric cone; Jordan algebra; diff-convex; filter method; interior point; JORDAN ALGEBRAS; NONCONVEX OPTIMIZATION; ALGORITHMS; SUM;

D O I：

10.1080/02331934.2011.585465

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：

We consider the extension of primal dual interior point methods for linear programming on symmetric cones, to a wider class of problems that includes approximate necessary optimality conditions for functions expressible as the difference of two convex functions of a special form. Our analysis applies the Jordan-algebraic approach to symmetric cones. As the basic method is local, we apply the idea of the filter method for a globalization strategy.

引用

页码：345 / 377

页数：33

共 50 条

[21] Reoptimization with the primal-dual interior point method
Gondzio, J
Grothey, A
[J]. SIAM JOURNAL ON OPTIMIZATION, 2003, 13 (03) : 842 - 864
[22] ON THE IMPLEMENTATION OF A PRIMAL-DUAL INTERIOR POINT METHOD
Mehrotra, Sanjay
[J]. SIAM JOURNAL ON OPTIMIZATION, 1992, 2 (04) : 575 - 601
[23] Parabolic target space and primal-dual interior-point methods
Nesterov, Yu.
[J]. DISCRETE APPLIED MATHEMATICS, 2008, 156 (11) : 2079 - 2100
[24] ON THE CONVERGENCE OF THE ITERATION SEQUENCE IN PRIMAL-DUAL INTERIOR-POINT METHODS
TAPIA, RA
ZHANG, Y
YE, YY
[J]. MATHEMATICAL PROGRAMMING, 1995, 68 (02) : 141 - 154
[25] SEMIDEFINITE PROGRAMMING: FORMULATIONS AND PRIMAL-DUAL INTERIOR-POINT METHODS
Fukuda, Mituhiro
Nakata, Maho
Yamashita, Makoto
[J]. REDUCED-DENSITY-MATRIX MECHANICS - WITH APPLICATION TO MANY-ELECTRON ATOMS AND MOLECULES, 2007, 134 : 103 - 118
[26] Inversion of Gravity Anomalies Using Primal-Dual Interior Point Methods
Zamora, Azucena
Velasco, Aaron A.
[J]. AIMS GEOSCIENCES, 2016, 2 (02): : 116 - 151
[27] Primal-dual Newton interior point methods in shape and topology optimization
Hoppe, RHW
Petrova, SI
[J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2004, 11 (5-6) : 413 - 429
[28] Generalization of Primal—Dual Interior-Point Methods to Convex Optimization Problems in Conic Form
Levent Tunçel
[J]. Foundations of Computational Mathematics, 2001, 1 : 229 - 254
[29] OPTIMAL PRIMAL-DUAL METHODS FOR A CLASS OF SADDLE POINT PROBLEMS
Chen, Yunmei
Lan, Guanghui
Ouyang, Yuyuan
[J]. SIAM JOURNAL ON OPTIMIZATION, 2014, 24 (04) : 1779 - 1814
[30] A Primal-dual Interior-point Algorithm for Symmetric Cone Convex Quadratic Programming Based on the Commutative Class Directions
S. Asadi
H. Mansouri
M. Zangiabadi
[J]. Acta Mathematicae Applicatae Sinica, English Series, 2019, 35 : 359 - 373

← 1 2 3 4 5 →