메뉴 건너뛰기




Volumn 20, Issue 5, 2010, Pages 2199-2227

Second-order analysis of polyhedral systems in finite and infinite dimensions with applications to robust stability of variational inequalities

Author keywords

Coderivatives and second order subdifferentials; Generalized differentiation; Parametric variational inequalities; Polyhedral sets; Reflexive Banach spaces; Robust stability; Variational analysis and optimization

Indexed keywords

GENERALIZED DIFFERENTIATION; POLYHEDRAL SET; REFLEXIVE BANACH SPACES; ROBUST STABILITY; SECOND ORDERS; VARIATIONAL ANALYSIS; VARIATIONAL INEQUALITIES;

EID: 77955421191     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/090766413     Document Type: Article
Times cited : (88)

References (30)
  • 1
    • 61349160550 scopus 로고    scopus 로고
    • A short algebraic proof of the Farkas lemma
    • D. Bartl, A short algebraic proof of the Farkas lemma, SIAM J. Optim., 19 (2008), pp. 234- 239.
    • (2008) SIAM J. Optim. , vol.19 , pp. 234-239
    • Bartl, D.1
  • 3
    • 0030521635 scopus 로고    scopus 로고
    • Characterizations of strong regularity for variational inequalities over polyhedral convex sets
    • A. L. Dontchev and R. T. Rockafellar, Characterizations of strong regularity for variational inequalities over polyhedral convex sets, SIAM J. Optim., 6 (1996), pp. 1087-1105.
    • (1996) SIAM J. Optim. , vol.6 , pp. 1087-1105
    • Dontchev, A.L.1    Rockafellar, R.T.2
  • 5
    • 55549091710 scopus 로고    scopus 로고
    • Coderivative calculus and metric regularity for constraint and variational systems
    • W. Geremew, B. S. Mordukhovich, and N. M. Nam, Coderivative calculus and metric regularity for constraint and variational systems, Nonlinear Anal., 70 (2009), pp. 529-552.
    • (2009) Nonlinear Anal. , vol.70 , pp. 529-552
    • Geremew, W.1    Mordukhovich, B.S.2    Nam, N.M.3
  • 6
    • 67349166166 scopus 로고    scopus 로고
    • On the coderivative of normal cone mappings to inequality systems
    • R. Henrion, J. V. Outrata, and T. Surowiec, On the coderivative of normal cone mappings to inequality systems, Nonlinear Anal., 71 (2009), pp. 1213-1226.
    • (2009) Nonlinear Anal. , vol.71 , pp. 1213-1226
    • Henrion, R.1    Outrata, J.V.2    Surowiec, T.3
  • 7
    • 84867976159 scopus 로고    scopus 로고
    • On M-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling
    • R. Henrion and W. Römisch, On M-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling, Appl. Math., 52 (2007), pp. 473-494.
    • (2007) Appl. Math. , vol.52 , pp. 473-494
    • Henrion, R.1    Römisch, W.2
  • 8
    • 0034361329 scopus 로고    scopus 로고
    • Metric regularity and subdifferential calculus
    • A. D. Ioffe, Metric regularity and subdifferential calculus, Russian Math. Surveys, 55 (2000), pp. 501-558.
    • (2000) Russian Math. Surveys , vol.55 , pp. 501-558
    • Ioffe, A.D.1
  • 10
    • 21044440287 scopus 로고    scopus 로고
    • Coderivatives in parametric optimization
    • A. B. Levy and B. S. Mordukhovich, Coderivatives in parametric optimization, Math. Prog., 99 (2004), pp. 311-327.
    • (2004) Math. Prog. , vol.99 , pp. 311-327
    • Levy, A.B.1    Mordukhovich, B.S.2
  • 11
    • 33646940121 scopus 로고
    • Maximum principle in the problem of time optimal control with nonsmooth constraints
    • B. S. Mordukhovich. Maximum principle in the problem of time optimal control with nonsmooth constraints, J. Appl. Math. Mech., 40 (1976), pp. 960-969.
    • (1976) J. Appl. Math. Mech. , vol.40 , pp. 960-969
    • Mordukhovich., B.S.1
  • 12
    • 0001254208 scopus 로고
    • Metric approximations and necessary optimality conditions for general classes of extremal problems
    • B. S. Mordukhovich, Metric approximations and necessary optimality conditions for general classes of extremal problems, Soviet Math. Dokl., 22 (1980), pp. 526-530.
    • (1980) Soviet Math. Dokl. , vol.22 , pp. 526-530
    • Mordukhovich, B.S.1
  • 13
    • 0026627404 scopus 로고
    • Sensitivity analysis in nonsmooth optimization
    • D. A. Field and V. Komkov, eds., SIAM, Philadelphia
    • B. S. Mordukhovich, Sensitivity analysis in nonsmooth optimization, in Theoretical Aspects of Industrial Design, Proc. Appl. Math. 58, D. A. Field and V. Komkov, eds., SIAM, Philadelphia, 1992, pp. 32-46.
    • (1992) Theoretical Aspects of Industrial Design, Proc. Appl. Math. , vol.58 , pp. 32-46
    • Mordukhovich, B.S.1
  • 14
    • 84966250815 scopus 로고
    • Complete characterizations of openness, metric regularity and Lipschitzian properties of multifunctions
    • B. S. Mordukhovich, Complete characterizations of openness, metric regularity and Lipschitzian properties of multifunctions, Trans. Amer. Math. Soc., 340 (1993), pp. 1-35.
    • (1993) Trans. Amer. Math. Soc. , vol.340 , pp. 1-35
    • Mordukhovich, B.S.1
  • 17
    • 0036348274 scopus 로고    scopus 로고
    • On second-order subdifferentials and their applications
    • B. S. Mordukhovich and J. V. Outrata, On second-order subdifferentials and their applications, SIAM J. Optim., 12 (2001), pp. 139-169.
    • (2001) SIAM J. Optim. , vol.12 , pp. 139-169
    • Mordukhovich, B.S.1    Outrata, J.V.2
  • 18
    • 43049169240 scopus 로고    scopus 로고
    • Coderivative analysis of quasi-variational inequalities with applications to stability and optimization
    • B. S. Mordukhovich and J. V. Outrata, Coderivative analysis of quasi-variational inequalities with applications to stability and optimization, SIAM J. Optim., 18 (2007), pp. 389- 412.
    • (2007) SIAM J. Optim. , vol.18 , pp. 389-412
    • Mordukhovich, B.S.1    Outrata, J.V.2
  • 19
    • 84938417111 scopus 로고    scopus 로고
    • Mathematical programs with equilibrium constraints: Theory and numerical methods
    • J. Haslinger and G. E. Stavroulakis, eds., Springer, New York
    • J. V. Outrata, Mathematical programs with equilibrium constraints: Theory and numerical methods, in Nonsmooth Mechanics of Solids, CISM Lecture Notes 485, J. Haslinger and G. E. Stavroulakis, eds., Springer, New York, 2006, pp. 221-274.
    • (2006) Nonsmooth Mechanics of Solids, CISM Lecture Notes , vol.485 , pp. 221-274
    • Outrata, J.V.1
  • 20
    • 58149165329 scopus 로고    scopus 로고
    • On the coderivative of the projection operator onto the secondorder cone
    • J. V. Outrata and D. Sun, On the coderivative of the projection operator onto the secondorder cone, Set-Valued Anal., 16 (2008), pp. 999-1014.
    • (2008) Set-Valued Anal. , vol.16 , pp. 999-1014
    • Outrata, J.V.1    Sun, D.2
  • 21
    • 0032222081 scopus 로고    scopus 로고
    • Tilt stability of a local minimum
    • R. A. Poliquin and R. T. Rockafellar, Tilt stability of a local minimum, SIAM J. Optim., 8 (1998), pp. 287-299.
    • (1998) SIAM J. Optim. , vol.8 , pp. 287-299
    • Poliquin, R.A.1    Rockafellar, R.T.2
  • 22
    • 13544252842 scopus 로고
    • The Lax-Milgram theorem for Banach spaces
    • S. Ramaswamy, The Lax-Milgram theorem for Banach spaces, Proc. Japan Acad. Ser. A. Math. Sci., 56 (1980), pp. 462-464.
    • (1980) Proc. Japan Acad. Ser. A. Math. Sci. , vol.56 , pp. 462-464
    • Ramaswamy, S.1
  • 24
    • 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
  • 27
    • 76549094566 scopus 로고    scopus 로고
    • Coderivative calculation related to a parametric affine variational inequality. Part 1: Basic calculations
    • J.-C. Yao and N. D. Yen, Coderivative calculation related to a parametric affine variational inequality. Part 1: Basic calculations, Acta Math. Vietnam., 34 (2009), pp. 157-172.
    • (2009) Acta Math. Vietnam. , vol.34 , pp. 157-172
    • Yao, J.-C.1    Yen, N.D.2
  • 28
    • 76549112631 scopus 로고    scopus 로고
    • Pointbased calculation related to a parametric affine variational inequality. Part 2: Applications
    • J.-C. Yao and N. D. Yen, Pointbased calculation related to a parametric affine variational inequality. Part 2: Applications, Pac. J. Optim., 5 (2009), pp. 493-506.
    • (2009) Pac. J. Optim. , vol.5 , pp. 493-506
    • Yao, J.-C.1    Yen, N.D.2
  • 29
    • 0034345391 scopus 로고    scopus 로고
    • Constraint qualifications and necessary optimality conditions for optimization problems with variational inequality constraints
    • J. J. Ye, Constraint qualifications and necessary optimality conditions for optimization problems with variational inequality constraints, SIAM J. Optim., 10 (2000), pp. 943-962.
    • (2000) SIAM J. Optim. , vol.10 , pp. 943-962
    • Ye, J.J.1
  • 30
    • 3042994369 scopus 로고
    • A generalization of the Farkas lemma and applications to convex programming
    • C. Zǎlinescu, A generalization of the Farkas lemma and applications to convex programming, J. Math. Anal. Appl., 66 (1978), pp. 651-678.
    • (1978) J. Math. Anal. Appl. , vol.66 , pp. 651-678
    • Zǎlinescu, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.