Differentiability v.s. convexity for complementarity functions

被引：4

作者：

Huang, Chien-Hao ^{[1
]}

Chen, Jein-Shan ^{[1
]}

Martinez-Legaz, Juan Enrique ^{[2
,3
]}

机构：

[1] Natl Taiwan Normal Univ, Dept Math, Taipei 11677, Taiwan

[2] Univ Autonoma Barcelona, Dept Econ & Hist Econ, Bellaterra 08193, Spain

[3] Barcelona Grad Sch Math, Barcelona, Spain

来源：

OPTIMIZATION LETTERS | 2017年 / 11卷 / 01期

基金：

澳大利亚研究理事会;

关键词：

Complementarity functions; NCP-functions; Second-order cone; Closed convex cone; 2ND-ORDER CONE; MERIT FUNCTIONS; MONOTONE;

D O I：

10.1007/s11590-015-0993-1

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：

It is known that complementarity functions play an important role in dealing with complementarity problems. The most well known complementarity problem is the symmetric cone complementarity problem (SCCP) which includes nonlinear complementarity problem (NCP), semidefinite complementarity problem (SDCP), and second-order cone complementarity problem (SOCCP) as special cases. Moreover, there is also so-called generalized complementarity problem (GCP) in infinite dimensional space. Among the existing NCP-functions, it was observed that there are no differentiable and convex NCP-functions. In particular, Miri and Effati (J Optim Theory Appl 164:723-730, 2015) show that convexity and differentiability cannot hold simultaneously for an NCP-function. In this paper, we further establish that such result also holds for general complementarity functions associated with the GCP.

引用

页码：209 / 216

页数：8

共 22 条

[1] [Anonymous], 2002, Convexity and optimization in Rn
[2] Two classes of merit functions for the second-order cone complementarity problem
Chen, Jein-Shan
[J]. MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2006, 64 (03) : 495 - 519
[3] The convex and monotone functions associated with second-order cone
Chen, Jein-Shan
[J]. OPTIMIZATION, 2006, 55 (04) : 363 - 385
[4] Chen JS, 2012, PAC J OPTIM, V8, P33
[5] Some characterizations for SOC-monotone and SOC-convex functions
Chen, Jein-Shan
Chen, Xin
Pan, Shaohua
Zhang, Jiawei
[J]. JOURNAL OF GLOBAL OPTIMIZATION, 2009, 45 (02) : 259 - 279
[6] An unconstrained smooth minimization reformulation of the second-order cone complementarity problem
Chen, JS
Tseng, P
[J]. MATHEMATICAL PROGRAMMING, 2005, 104 (2-3) : 293 - 327
[7] Characterizations for solidness of dual cones with applications
Chiang, Y.
[J]. JOURNAL OF GLOBAL OPTIMIZATION, 2012, 52 (01) : 79 - 94
[8] Cottle R.W., 1992, The Linear Complementarity Problem
[9] Facchinei Francisco, 2003, SPRINGER SERIES OPER
[10] Faraut J., 1994, Oxford Math. Monogr.

← 1 2 3 →