메뉴 건너뛰기




Volumn 13, Issue 2, 2003, Pages 368-385

Complementarity constraint qualification via the theory of 2-regularity

Author keywords

2 regularity; Constraint qualification; Equilibrium constraints; Optimality conditions; Tangent cone

Indexed keywords


EID: 0038811726     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623499365292     Document Type: Article
Times cited : (6)

References (20)
  • 1
    • 0003038818 scopus 로고
    • Extremum conditions for smooth problems with equality-type constraints
    • E.R. AVAKOV, Extremum conditions for smooth problems with equality-type constraints, Comput. Math. Math. Phys., 25 (1985), pp. 24-32.
    • (1985) Comput. Math. Math. Phys. , vol.25 , pp. 24-32
    • Avakov, E.R.1
  • 2
    • 0001035398 scopus 로고
    • Necessary extremum conditions for smooth abnormal problems with equality and inequality constraints
    • E.R. AVAKOV, Necessary extremum conditions for smooth abnormal problems with equality and inequality constraints, Math. Notes, 45 (1989), pp. 431-437.
    • (1989) Math. Notes , vol.45 , pp. 431-437
    • Avakov, E.R.1
  • 3
    • 0020167088 scopus 로고
    • A unified theory of first- and second-order optimality conditions for extremum problems in topological vector spaces
    • J.F. BEN-TAL AND J. ZOWE, A unified theory of first- and second-order optimality conditions for extremum problems in topological vector spaces, Math. Programming Stud., 19 (1982), pp. 39-76.
    • (1982) Math. Programming Stud. , vol.19 , pp. 39-76
    • Ben-Tal, J.F.1    Zowe, J.2
  • 4
    • 84863041059 scopus 로고
    • The nonlinear bilevel programming problem: Formulations, regularity and optimality conditions
    • Y. CHEN AND M. FLORIAN, The nonlinear bilevel programming problem: Formulations, regularity and optimality conditions, Optimization, 32 (1995), pp. 193-209.
    • (1995) Optimization , vol.32 , pp. 193-209
    • Chen, Y.1    Florian, M.2
  • 5
    • 0000204124 scopus 로고    scopus 로고
    • On certain generalizations of Morse's lemma
    • A.F. IZMAILOV, On certain generalizations of Morse's lemma, Proc. Steklov Inst. Math., 220 (1998), pp. 138-153.
    • (1998) Proc. Steklov Inst. Math. , vol.220 , pp. 138-153
    • Izmailov, A.F.1
  • 6
    • 0036671134 scopus 로고    scopus 로고
    • The theory of 2-regularity for mappings with Lipschitzian derivatives and its applications to optimality conditions
    • to appear
    • A.F. IZMAILOV AND M.V. SOLODOV, The theory of 2-regularity for mappings with Lipschitzian derivatives and its applications to optimality conditions, Math. Oper. Res., (2002), to appear.
    • (2002) Math. Oper. Res.
    • Izmailov, A.F.1    Solodov, M.V.2
  • 7
    • 0005342454 scopus 로고    scopus 로고
    • Error bounds for 2-regular mappings with Lipschitzian derivatives and their applications
    • A.F. IZMAILOV AND M.V. SOLODOV, Error bounds for 2-regular mappings with Lipschitzian derivatives and their applications, Math, Program., 89 (2001), pp. 413-435.
    • (2001) Math, Program. , vol.89 , pp. 413-435
    • Izmailov, A.F.1    Solodov, M.V.2
  • 8
    • 0036338484 scopus 로고    scopus 로고
    • Optimality conditions for irregular inequality-constrained problems
    • A.F. IZMAILOV AND M.V. SOLODOV, Optimality conditions for irregular inequality-constrained problems, SIAM J. Control Optim., 40 (2001), pp. 1280-1295.
    • (2001) SIAM J. Control Optim. , vol.40 , pp. 1280-1295
    • Izmailov, A.F.1    Solodov, M.V.2
  • 9
    • 0032154102 scopus 로고    scopus 로고
    • High-order approximations and generalized necessary conditions for optimality
    • U. LEDZEWICZ AND H. SCHÄTTLER, High-order approximations and generalized necessary conditions for optimality, SIAM J. Control Optim., 37 (1998), pp. 33-53.
    • (1998) SIAM J. Control Optim. , vol.37 , pp. 33-53
    • Ledzewicz, U.1    Schättler, H.2
  • 11
    • 0041540601 scopus 로고    scopus 로고
    • Exact penalization and stationarity conditions of mathematical programs with equilibrium constraints
    • Z.-Q. Luo, J.-S. PANG, D. RALPH, AND S.-Q. Wu, Exact penalization and stationarity conditions of mathematical programs with equilibrium constraints, Math. Programming, 75 (1996), pp. 19-76.
    • (1996) Math. Programming , vol.75 , pp. 19-76
    • Luo, Z.-Q.1    Pang, J.-S.2    Ralph, D.3    Wu, S.-Q.4
  • 12
    • 0002330898 scopus 로고
    • On the local structure of the zero-set of a Banach space valued mapping
    • R. J. MAGNUS, On the local structure of the zero-set of a Banach space valued mapping, J. Funct. Anal., 22 (1976), pp. 58-72.
    • (1976) J. Funct. Anal. , vol.22 , pp. 58-72
    • Magnus, R.J.1
  • 13
    • 49949133603 scopus 로고
    • The Fritz John necessary optimality conditions in the presence of equality and inequality constraints
    • O.L. MANGASARIAN AND S. FROMOVITZ, The Fritz John necessary optimality conditions in the presence of equality and inequality constraints, J. Math. Anal. Appl., 7 (1967), pp. 37-47.
    • (1967) J. Math. Anal. Appl. , vol.7 , pp. 37-47
    • Mangasarian, O.L.1    Fromovitz, S.2
  • 14
    • 0033359013 scopus 로고    scopus 로고
    • Optimality conditions for a class of mathematical programs with equilibrium constraints
    • J.V. OUTRATA, Optimality conditions for a class of mathematical programs with equilibrium constraints, Math. Oper. Res., 24 (1999), pp. 627-644.
    • (1999) Math. Oper. Res. , vol.24 , pp. 627-644
    • Outrata, J.V.1
  • 15
    • 0000181946 scopus 로고    scopus 로고
    • Complementarity constraint qualifications and simplified B-stationarity conditions for mathematical programs with equilibrium constraints
    • J.-S. PANG AND M. FUKUSHIMA, Complementarity constraint qualifications and simplified B-stationarity conditions for mathematical programs with equilibrium constraints, Comput. Optim. Appl., 13 (1999), pp. 111-136.
    • (1999) Comput. Optim. Appl. , vol.13 , pp. 111-136
    • Pang, J.-S.1    Fukushima, M.2
  • 16
    • 0032154380 scopus 로고    scopus 로고
    • Second-order conditions for optimization problems with constraints
    • J.-P. PENOT, Second-order conditions for optimization problems with constraints, SIAM J. Control Optim., 37 (1999), pp. 303-318.
    • (1999) SIAM J. Control Optim. , vol.37 , pp. 303-318
    • Penot, J.-P.1
  • 17
    • 0018977011 scopus 로고
    • Strongly regular generalized equations
    • S.M. ROBINSON. Strongly regular generalized equations, Math. Oper. Res., 5 (1980). pp. 43-62.
    • (1980) Math. Oper. Res. , vol.5 , pp. 43-62
    • Robinson, S.M.1
  • 18
    • 0034139059 scopus 로고    scopus 로고
    • Mathematical programs with complementarity constraints: Stationarity, optimality and sensitivity
    • H. SCHEEL AND S. SCHOLTES, Mathematical programs with complementarity constraints: Stationarity, optimality and sensitivity, Math. Oper. Res., 25 (2000), pp. 1-22.
    • (2000) Math. Oper. Res. , vol.25 , pp. 1-22
    • Scheel, H.1    Scholtes, S.2
  • 19
    • 0000200095 scopus 로고
    • Necessary and sufficient conditions for optimality of pth order
    • A.A. TRETYAKOV, Necessary and sufficient conditions for optimality of pth order, Comput. Math. Math. Phys., 24 (1984), pp. 123-127.
    • (1984) Comput. Math. Math. Phys. , vol.24 , pp. 123-127
    • Tretyakov, A.A.1
  • 20
    • 0033439649 scopus 로고    scopus 로고
    • Optimality conditions for optimization problems with complementarity constraints
    • J.J. YE, Optimality conditions for optimization problems with complementarity constraints, SIAM J. Optim., 9 (1999), pp. 374-387.
    • (1999) SIAM J. Optim. , vol.9 , pp. 374-387
    • Ye, J.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.