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Volumn 78, Issue 267, 2009, Pages 1671-1686

Combined Monte Carlo sampling and penalty method for stochastic nonlinear complementarity problems

Author keywords

Convergence; Monte Carlo method; Penalization; Recourse; Stochastic nonlinear complementarity problem

Indexed keywords


EID: 67749110170     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-09-02206-6     Document Type: Article
Times cited : (21)

References (30)
  • 1
    • 33847039571 scopus 로고    scopus 로고
    • Solving stochastic mathematical programs with complementarity constraints using simulation
    • MR2281227 (2007k:90073)
    • S.I. Birbil, G. G̈urkan, and O. Listes, Solving stochastic mathematical programs with complementarity constraints using simulation, Mathematics of Operations Research, 31 (2006), 739-760. MR2281227 (2007k:90073)
    • (2006) Mathematics of Operations Research , vol.31 , pp. 739-760
    • Birbil, S.I.1    Gürkan, G.2    Listes, O.3
  • 2
    • 33745712333 scopus 로고    scopus 로고
    • Convergence theory for nonconvex stochastic programming with an application to mixed logit
    • MR2238700 (2007c:90061)
    • F. Bastin, C. Cirillo and P.L. Toint, Convergence theory for nonconvex stochastic programming with an application to mixed logit, Mathematical Programming, 108 (2006), 207-234. MR2238700 (2007c:90061)
    • (2006) Mathematical Programming , vol.108 , pp. 207-234
    • Bastin, F.1    Cirillo, C.2    Toint, P.L.3
  • 4
    • 0035529806 scopus 로고    scopus 로고
    • 0-type and monotone nonlinear complementarity problems
    • MR1824294 (2001m:90107)
    • 0-type and monotone nonlinear complementarity problems, Journal of Optimization Theory and Applications, 108 (2001), 297-316. MR1824294 (2001m:90107)
    • (2001) Journal of Optimization Theory and Applications , vol.108 , pp. 297-316
    • Chen, B.1
  • 5
    • 0031493118 scopus 로고    scopus 로고
    • Smooth approximations to nonlinear complementarity problems
    • MR1443626 (98e:90192)
    • B. Chen and P.T. Harker, Smooth approximations to nonlinear complementarity problems, SIAM Journal on Optimization, 7 (1997), 403-420. MR1443626 (98e:90192)
    • (1997) SIAM Journal on Optimization , vol.7 , pp. 403-420
    • Chen, B.1    Harker, P.T.2
  • 6
    • 31144459305 scopus 로고    scopus 로고
    • Expected residual minimization method for stochastic linear complementarity problems
    • MR2185828 (2006h:90069)
    • X. Chen and M. Fukushima, Expected residual minimization method for stochastic linear complementarity problems, Mathematics of Operations Research, 30 (2005), 1022-1038. MR2185828 (2006h:90069)
    • (2005) Mathematics of Operations Research , vol.30 , pp. 1022-1038
    • Chen, X.1    Fukushima, M.2
  • 7
    • 46749143296 scopus 로고    scopus 로고
    • Robust solution of monotone stochastic linear complementarity problems
    • X. Chen, C. Zhang and M. Fukushima, Robust solution of monotone stochastic linear complementarity problems, Mathematical Programming, 117 (2009), 51-80.
    • (2009) Mathematical Programming , vol.117 , pp. 51-80
    • Chen, X.1    Zhang, C.2    Fukushima, M.3
  • 8
    • 84863041059 scopus 로고
    • The nonlinear bilevel programming problem: Formulations, regularity and optimality conditions
    • MR1336341 (96c:90100)
    • Y. Chen and M. Florian, The nonlinear bilevel programming problem: Formulations, regularity and optimality conditions, Optimization, 32 (1995), 193-209. MR1336341 (96c:90100)
    • (1995) Optimization , vol.32 , pp. 193-209
    • Chen, Y.1    Florian, M.2
  • 12
    • 0007954921 scopus 로고    scopus 로고
    • Sample-path solution of stochastic variational inequalities
    • MR1690005 (2000b:90094)
    • G. Gürkan, A.Y. Özge and S.M. Robinson, Sample-path solution of stochastic variational inequalities, Mathematical Programming, 84 (1999), 313-333. MR1690005 (2000b:90094)
    • (1999) Mathematical Programming , vol.84 , pp. 313-333
    • Gürkan, G.1    Özge, A.Y.2    Robinson, S.M.3
  • 13
    • 0027657329 scopus 로고
    • Semi-infinite programming: Theory, methods, and applications
    • MR1234637 (94g:90152)
    • R. Hettich and K.O. Kortanek, Semi-infinite programming: Theory, methods, and applications, SIAM Review, 35 (1993), 380-429. MR1234637 (94g:90152)
    • (1993) SIAM Review , vol.35 , pp. 380-429
    • Hettich, R.1    Kortanek, K.O.2
  • 14
    • 35148884635 scopus 로고    scopus 로고
    • New restricted NCP function and their applications to stochastic NCP and stochastic MPEC
    • MR2362712 (2008g:90068)
    • G.H. Lin, X. Chen and M. Fukushima, New restricted NCP function and their applications to stochastic NCP and stochastic MPEC, Optimization, 56 (2007), 641-753. MR2362712 (2008g:90068)
    • (2007) Optimization , vol.56 , pp. 641-753
    • Lin, G.H.1    Chen, X.2    Fukushima, M.3
  • 15
    • 45749085726 scopus 로고    scopus 로고
    • Solving stochastic mathematical programs with equilibrium constraints via approximation and smoothing implicit programming with penalization
    • G.H. Lin, X. Chen and M. Fukushima, Solving stochastic mathematical programs with equilibrium constraints via approximation and smoothing implicit programming with penalization, Mathematical Programming, 116 (2009), 343-368.
    • (2009) Mathematical Programming , vol.116 , pp. 343-368
    • Lin, G.H.1    Chen, X.2    Fukushima, M.3
  • 16
    • 33745603601 scopus 로고    scopus 로고
    • A class of stochastic mathematical programs with complementarity constraints: Reformulations and algorithms
    • MR2127807 (2006d:90111)
    • G.H. Lin and M. Fukushima, A class of stochastic mathematical programs with complementarity constraints: Reformulations and algorithms, Journal of Industrial and Management Optimization, 1 (2005), 99-122. MR2127807 (2006d:90111)
    • (2005) Journal of Industrial and Management Optimization , vol.1 , pp. 99-122
    • Lin, G.H.1    Fukushima, M.2
  • 17
    • 33745616495 scopus 로고    scopus 로고
    • New reformulations for stochastic complementarity problems
    • MR2277498 (2007j:90036)
    • G.H. Lin and M. Fukushima, New reformulations for stochastic complementarity problems, Optimization Methods and Software, 21 (2006), 551-564. MR2277498 (2007j:90036)
    • (2006) Optimization Methods and Software , vol.21 , pp. 551-564
    • Lin, G.H.1    Fukushima, M.2
  • 18
    • 30844467532 scopus 로고    scopus 로고
    • Regularization method for stochastic mathematical programs with complementarity constraints, European Series of Applied and Industrial Mathematics (ESAIM): Control
    • MR2141889 (2005m:90073)
    • G.H. Lin and M. Fukushima, Regularization method for stochastic mathematical programs with complementarity constraints, European Series of Applied and Industrial Mathematics (ESAIM): Control, Optimisation and Calculus of Variations, 11 (2005), 252-265. MR2141889 (2005m:90073)
    • (2005) Optimisation and Calculus of Variations , vol.11 , pp. 252-265
    • Lin, G.H.1    Fukushima, M.2
  • 19
    • 43949118453 scopus 로고    scopus 로고
    • Monte Carlo and quasi-Monte Carlo sampling methods for a class of stochastic mathematical programs with equilibrium constraints
    • MR2403716
    • G.H. Lin, H. Xu and M. Fukushima, Monte Carlo and quasi-Monte Carlo sampling methods for a class of stochastic mathematical programs with equilibrium constraints, Mathematical Methods of Operations Research, 67 (2008), 423-441. MR2403716
    • (2008) Mathematical Methods of Operations Research , vol.67 , pp. 423-441
    • Lin, G.H.1    Xu, H.2    Fukushima, M.3
  • 21
    • 34547948140 scopus 로고    scopus 로고
    • A regularized sample average approximation method for stochastic mathematical programs with nonsmooth equality constraints
    • MR2257215 (2007i:90051)
    • F. Meng and H. Xu, A regularized sample average approximation method for stochastic mathematical programs with nonsmooth equality constraints, SIAM Journal on Optimization, 17 (2006), 891-919. MR2257215 (2007i:90051)
    • (2006) SIAM Journal on Optimization , vol.17 , pp. 891-919
    • Meng, F.1    Xu, H.2
  • 22
    • 33846136710 scopus 로고    scopus 로고
    • Exponential convergence of sample average approximation methods for a class of stochastic mathematical programs with complementarity constraints
    • MR2269956 (2007g:90068)
    • F. Meng and H. Xu, Exponential convergence of sample average approximation methods for a class of stochastic mathematical programs with complementarity constraints, Journal of Computational Mathematics, 24 (2006), 733-748. MR2269956 (2007g:90068)
    • (2006) Journal of Computational Mathematics , vol.24 , pp. 733-748
    • Meng, F.1    Xu, H.2
  • 23
    • 0004734119 scopus 로고
    • Random Number Generation and Quasi-Monte Carlo Methods
    • MR1172997 (93h:65008)
    • H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992. MR1172997 (93h:65008)
    • (1992) SIAM, Philadelphia
    • Niederreiter, H.1
  • 26
    • 31144457268 scopus 로고    scopus 로고
    • Stochastic programming with equilibrium constraints
    • MR2201897 (2006j:90054)
    • A. Shapiro, Stochastic programming with equilibrium constraints, Journal of Optimization Theory and Applications, 128 (2006), 223-243. MR2201897 (2006j:90054)
    • (2006) Journal of Optimization Theory and Applications , vol.128 , pp. 223-243
    • Shapiro, A.1
  • 27
    • 42549162441 scopus 로고    scopus 로고
    • Stochastic mathematical programs with equilibrium constraints, modelling and sample average approximation
    • MR2412074
    • A. Shapiro and H. Xu, Stochastic mathematical programs with equilibrium constraints, modelling and sample average approximation, Optimization, 57 (2008), 395-418. MR2412074
    • (2008) Optimization , vol.57 , pp. 395-418
    • Shapiro, A.1    Xu, H.2
  • 28
    • 33745609926 scopus 로고    scopus 로고
    • An implicit programming approach for a class of stochastic mathematical programs with linear complementarity constraints
    • MR2197552 (2006k:90086)
    • H. Xu, An implicit programming approach for a class of stochastic mathematical programs with linear complementarity constraints, SIAM Journal on Optimization, 16 (2006), 670-696. MR2197552 (2006k:90086)
    • (2006) SIAM Journal on Optimization , vol.16 , pp. 670-696
    • Xu, H.1
  • 29
    • 38549128325 scopus 로고    scopus 로고
    • Convergence analysis of sample average approximation methods for a class of stochastic mathematical programs with equality constraints
    • MR2348240 (2008h:90068)
    • H. Xu and F. Meng, Convergence analysis of sample average approximation methods for a class of stochastic mathematical programs with equality constraints, Mathematics of Operations Research, 32 (2007), 648-668. MR2348240 (2008h:90068)
    • (2007) Mathematics of Operations Research , vol.32 , pp. 648-668
    • Xu, H.1    Meng, F.2
  • 30
    • 42449113697 scopus 로고    scopus 로고
    • Stochastic nonlinear complementarity problem and applications to traffic equilibrium under uncertainty
    • MR2395102
    • C. Zhang and X. Chen, Stochastic nonlinear complementarity problem and applications to traffic equilibrium under uncertainty, Journal of Optimization Theory and Applications, 137 (2008), 277-295. MR2395102
    • (2008) Journal of Optimization Theory and Applications , vol.137 , pp. 277-295
    • Zhang, C.1    Chen, X.2


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