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Volumn 146, Issue 2, 2010, Pages 419-443

Feasible Method for Generalized Semi-Infinite Programming

Author keywords

Bilevel programming; Design centering; Interior point method; Mathematical program with equilibrium constraints; Semi infinite programming

Indexed keywords

APPROXIMATION ALGORITHMS; MATHEMATICAL PROGRAMMING;

EID: 77955986795     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-010-9674-5     Document Type: Article
Times cited : (18)

References (37)
  • 1
    • 1642417653 scopus 로고    scopus 로고
    • Solving semi-infinite optimization problems with interior point techniques
    • Stein, O., Still, G.: Solving semi-infinite optimization problems with interior point techniques. SIAM J. Control Optim. 42, 769-788 (2003).
    • (2003) SIAM J. Control Optim. , vol.42 , pp. 769-788
    • Stein, O.1    Still, G.2
  • 2
    • 54949122903 scopus 로고    scopus 로고
    • The adaptive convexification algorithm: A feasible point method for semi-infinite programming
    • Floudas, C. A., Stein, O.: The adaptive convexification algorithm: a feasible point method for semi-infinite programming. SIAM J. Optim. 18, 1187-1208 (2007).
    • (2007) SIAM J. Optim. , vol.18 , pp. 1187-1208
    • Floudas, C.A.1    Stein, O.2
  • 5
    • 84976505772 scopus 로고    scopus 로고
    • A semi-infinite approach to design centering
    • S. Dempe and V. Kalashnikov (Eds.), Berlin: Springer
    • Stein, O.: A semi-infinite approach to design centering. In: Dempe, S., Kalashnikov, V. (eds.) Optimization with Multivalued Mappings, pp. 209-228. Springer, Berlin (2006).
    • (2006) Optimization with Multivalued Mappings , pp. 209-228
    • Stein, O.1
  • 6
    • 77955990891 scopus 로고    scopus 로고
    • Winterfeld, A.: Large-scale semi-infinite optimization applied to industrial gemstone cutting. PhD thesis, TU Kaiserslautern (2007).
  • 7
    • 0023961719 scopus 로고
    • The acceleration radius: A global performance measure for robotic manipulators
    • Graettinger, T. J., Krogh, B. H.: The acceleration radius: a global performance measure for robotic manipulators. IEEE J. Robot. Autom. 4, 60-69 (1988).
    • (1988) IEEE J. Robot. Autom. , vol.4 , pp. 60-69
    • Graettinger, T.J.1    Krogh, B.H.2
  • 9
    • 0015571360 scopus 로고
    • Directional derivatives for extremal value functions with applications to the completely convex case
    • Hogan, W. W.: Directional derivatives for extremal value functions with applications to the completely convex case. Oper. Res. 21, 188-209 (1973).
    • (1973) Oper. Res. , vol.21 , pp. 188-209
    • Hogan, W.W.1
  • 11
    • 0036833064 scopus 로고    scopus 로고
    • On generalized semi-infinite optimization and bilevel optimization
    • Stein, O., Still, G.: On generalized semi-infinite optimization and bilevel optimization. Eur. J. Oper. Res. 142, 444-462 (2002).
    • (2002) Eur. J. Oper. Res. , vol.142 , pp. 444-462
    • Stein, O.1    Still, G.2
  • 13
    • 0031352141 scopus 로고    scopus 로고
    • Engineering and economic applications of complementarity problems
    • Ferris, M. C., Pang, J. S.: Engineering and economic applications of complementarity problems. SIAM Rev. 39(4), 669-713 (1997).
    • (1997) SIAM Rev. , vol.39 , Issue.4 , pp. 669-713
    • Ferris, M.C.1    Pang, J.S.2
  • 14
    • 0042737841 scopus 로고    scopus 로고
    • Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints
    • Dempe, S.: Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints. Optimization 52(3), 333-359 (2003).
    • (2003) Optimization , vol.52 , Issue.3 , pp. 333-359
    • Dempe, S.1
  • 15
    • 77956000720 scopus 로고    scopus 로고
    • Pieper, H.: Algorithms for mathematical programs with equilibrium constraints with applications to deregulated electricity markets. PhD thesis, Stanford University (2001).
  • 16
    • 0034139059 scopus 로고    scopus 로고
    • Mathematical programs with complementarity constraints: Stationarity, optimality, and sensitivity
    • Scheel, H., Scholtes, S.: Mathematical programs with complementarity constraints: stationarity, optimality, and sensitivity. Math. Oper. Res. 25, 1-22 (2000).
    • (2000) Math. Oper. Res. , vol.25 , pp. 1-22
    • Scheel, H.1    Scholtes, S.2
  • 17
    • 0013468401 scopus 로고
    • Nonlinear optimization: Characterization of structural stability
    • Jongen, H. Th., Weber, G.-W.: Nonlinear optimization: Characterization of structural stability. J. Global Optim. 1, 47-64 (1991).
    • (1991) J. Global Optim. , vol.1 , pp. 47-64
    • Jongen, H.T.1    Weber, G.-W.2
  • 18
    • 77956006397 scopus 로고    scopus 로고
    • Fletcher, R., Leyffer, S.: Numerical experience with solving mpecs as nlps. Technical Report NA/210, University of Dundee (2002).
  • 19
    • 0029206129 scopus 로고
    • Smoothing methods for convex inequalities and linear complementarity problems
    • Chen, C., Mangasarian, O. L.: Smoothing methods for convex inequalities and linear complementarity problems. Math. Program. 71(1), 51-69 (1995).
    • (1995) Math. Program. , vol.71 , Issue.1 , pp. 51-69
    • Chen, C.1    Mangasarian, O.L.2
  • 20
    • 0000425448 scopus 로고    scopus 로고
    • A smoothing method for mathematical programs with equilibrium constraints
    • Facchinei, F., Jiang, H., Qi, L.: A smoothing method for mathematical programs with equilibrium constraints. Math. Program. 85(1), 107-134 (1999).
    • (1999) Math. Program. , vol.85 , Issue.1 , pp. 107-134
    • Facchinei, F.1    Jiang, H.2    Qi, L.3
  • 21
    • 0034399526 scopus 로고    scopus 로고
    • Smooth SQP methods for mathematical programs with nonlinear complementarity constraints
    • Jiang, H., Ralph, D.: Smooth SQP methods for mathematical programs with nonlinear complementarity constraints. SIAM J. Optim. 10(3), 779-808 (2000).
    • (2000) SIAM J. Optim. , vol.10 , Issue.3 , pp. 779-808
    • Jiang, H.1    Ralph, D.2
  • 22
    • 15244359760 scopus 로고    scopus 로고
    • A modified relaxation scheme for mathematical programs with complementarity constraints
    • Lin, G.-H., Fukushima, M.: A modified relaxation scheme for mathematical programs with complementarity constraints. Ann. Oper. Res. 133(22), 63-84 (2005).
    • (2005) Ann. Oper. Res. , vol.133 , Issue.22 , pp. 63-84
    • Lin, G.-H.1    Fukushima, M.2
  • 23
    • 9944252900 scopus 로고    scopus 로고
    • Lower-order penalty methods for mathematical programs with complementarity constraints
    • Yang, X. Q., Huang, X. X.: Lower-order penalty methods for mathematical programs with complementarity constraints. Optim. Methods Softw. 19(6), 693-720 (2004).
    • (2004) Optim. Methods Softw. , vol.19 , Issue.6 , pp. 693-720
    • Yang, X.Q.1    Huang, X.X.2
  • 24
    • 0037394962 scopus 로고    scopus 로고
    • Extension of quasi-newton methods to mathematical programs with complementarity constraints
    • Jiang, H., Ralph, D.: Extension of quasi-newton methods to mathematical programs with complementarity constraints. Comput. Optim. Appl. 25(1-3), 123-150 (2003).
    • (2003) Comput. Optim. Appl. , vol.25 , Issue.1-3 , pp. 123-150
    • Jiang, H.1    Ralph, D.2
  • 25
    • 77955986928 scopus 로고    scopus 로고
    • Stein, O.: Lifting mathematical programs with complementarity constraints. Math. Program. (2010, to appear).
  • 26
    • 77956005267 scopus 로고    scopus 로고
    • Ferris, M. C., Kanzow, C.: Complementarity and related problems: A survey. In: Handbook of Applied Optimization, pp. 514-530 (2002).
  • 27
  • 28
    • 33846167695 scopus 로고    scopus 로고
    • On Karush-Kuhn-Tucker points for a smoothing method in semi-infinite optimization
    • Stein, O.: On Karush-Kuhn-Tucker points for a smoothing method in semi-infinite optimization. J. Comput. Math. 24, 719-732 (2006).
    • (2006) J. Comput. Math. , vol.24 , pp. 719-732
    • Stein, O.1
  • 29
    • 0007291852 scopus 로고    scopus 로고
    • A branch-and-bound approach for solving a class of generalized semi-infinite programming problems
    • Levitin, E., Tichatschke, R.: A branch-and-bound approach for solving a class of generalized semi-infinite programming problems. J. Global Optim. 13, 299-315 (1998).
    • (1998) J. Global Optim. , vol.13 , pp. 299-315
    • Levitin, E.1    Tichatschke, R.2
  • 31
    • 0026850425 scopus 로고
    • On the classical logarithmic barrier function method for a class of smooth convex programming problems
    • Den Hertog, D., Roos, C., Terlaky, T.: On the classical logarithmic barrier function method for a class of smooth convex programming problems. J. Optim. Theory Appl. 73(1), 1-25 (1992).
    • (1992) J. Optim. Theory Appl. , vol.73 , Issue.1 , pp. 1-25
    • Den Hertog, D.1    Roos, C.2    Terlaky, T.3
  • 32
    • 53349118612 scopus 로고    scopus 로고
    • Smoothing methods for convex inequalities and linear complementarity problems
    • Izmailov, A. F., Solodov, M. V.: Smoothing methods for convex inequalities and linear complementarity problems. Lect. Not. Econ. Math. Syst. 563, 133-145 (2006).
    • (2006) Lect. Not. Econ. Math. Syst. , vol.563 , pp. 133-145
    • Izmailov, A.F.1    Solodov, M.V.2
  • 33
    • 0032552250 scopus 로고    scopus 로고
    • A global optimization method, αBB, for general twice-differentiable constrained NLPs-I: Theoretical advances
    • Adjiman, C. S., Androulakis, I. P., Floudas, C. A.: A global optimization method, αBB, for general twice-differentiable constrained NLPs-I: Theoretical advances. Comput. Chem. Eng. 22, 1137-1158 (1998).
    • (1998) Comput. Chem. Eng. , vol.22 , pp. 1137-1158
    • Adjiman, C.S.1    Androulakis, I.P.2    Floudas, C.A.3
  • 34
    • 0032552252 scopus 로고    scopus 로고
    • A global optimization method, αBB, for general twice-differentiable constrained NLPs-II: Implementation and computational results
    • Adjiman, C. S., Androulakis, I. P., Floudas, C. A.: A global optimization method, αBB, for general twice-differentiable constrained NLPs-II: Implementation and computational results. Comput. Chem. Eng. 22, 1159-1179 (1998).
    • (1998) Comput. Chem. Eng. , vol.22 , pp. 1159-1179
    • Adjiman, C.S.1    Androulakis, I.P.2    Floudas, C.A.3
  • 36
    • 77956002022 scopus 로고    scopus 로고
    • Adaptive convexification in semi-infinite optimization
    • 2nd edn., P. M. Pardalos and C. A. Floudas (Eds.), Berlin: Springer
    • Stein, O.: Adaptive convexification in semi-infinite optimization. In: Pardalos, P. M., Floudas, C. A. (eds.) Encyclopedia of Optimization, Part 1, 2nd edn., pp. 13-19. Springer, Berlin (2009).
    • (2009) Encyclopedia of Optimization, Part 1 , pp. 13-19
    • Stein, O.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.