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Volumn 121, Issue 3, 2004, Pages 647-671

On constraint qualifications in nonsmooth optimization

Author keywords

alternative theorems; constraint qualifications; convexity; Nonsmooth optimization; optimality conditions; reverse convexity; semi infinite optimization

Indexed keywords

ALTERNATIVE THEOREM; CONSTRAINT QUALIFICATION; CONVEX PROBLEMS; CONVEXITY; FIRST-ORDER OPTIMALITY CONDITION; NONSMOOTH OPTIMIZATION; NONSMOOTH OPTIMIZATION PROBLEMS; OPTIMALITY CONDITIONS; REVERSE CONVEXITY; SEMI-INFINITE OPTIMIZATION;

EID: 4444286112     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOTA.0000037607.48762.45     Document Type: Review
Times cited : (27)

References (48)
  • 1
    • 34249953633 scopus 로고
    • General Constraint Qualifications in Nondifferentiable Programming
    • MERKOVSKY, R. R., and WARD, D. E., General Constraint Qualifications in Nondifferentiable Programming, Mathematical Programming, Vol. 47, pp. 389-405, 1990.
    • (1990) Mathematical Programming , vol.47 , pp. 389-405
    • Merkovsky, R.R.1    Ward, D.E.2
  • 2
    • 0012088834 scopus 로고
    • A Constraint Qualification in Quasidifferentiable Programming
    • WARD, D. E., A Constraint Qualification in Quasidifferentiable Programming, Optimization, Vol. 22, pp. 661-668, 1991.
    • (1991) Optimization , vol.22 , pp. 661-668
    • Ward, D.E.1
  • 3
    • 34250078579 scopus 로고
    • Constraint Qualifications is in Quasidifferentiable Optimization
    • KUNTZ, L., and SCHOLTES, S., Constraint Qualifications is in Quasidifferentiable Optimization, Mathematical Programming, Vol. 60, pp. 339-347, 1993.
    • (1993) Mathematical Programming , vol.60 , pp. 339-347
    • Kuntz, L.1    Scholtes, S.2
  • 5
    • 0028449086 scopus 로고
    • Constraint Qualifications and Lagrange Multipliers in Nondifferentiable Programming Problems
    • JOURANI, A., Constraint Qualifications and Lagrange Multipliers in Nondifferentiable Programming Problems, Journal of Optimization Theory and Applications, Vol. 81, pp. 533-548, 1994.
    • (1994) Journal of Optimization Theory and Applications , vol.81 , pp. 533-548
    • Jourani, A.1
  • 6
    • 0028464574 scopus 로고
    • A Nonsmooth Variant of the Mangasarian-Fromovitz Constraint Qualification
    • KUNTZ, L., and SCHOLTES, S., A Nonsmooth Variant of the Mangasarian-Fromovitz Constraint Qualification, Journal of Optimization Theory and Applications, Vol. 82, pp. 59-75, 1994.
    • (1994) Journal of Optimization Theory and Applications , vol.82 , pp. 59-75
    • Kuntz, L.1    Scholtes, S.2
  • 11
    • 49949133603 scopus 로고
    • The Fritz John Necessary Optimality Conditions in the Presence of Equality and Inequality Constraints
    • MANGASARIAN, O. L., and FROMOVITZ, S., The Fritz John Necessary Optimality Conditions in the Presence of Equality and Inequality Constraints, Journal of Mathematical Analysis and Applications, Vol. 17, pp. 37-47, 1967.
    • (1967) Journal of Mathematical Analysis and Applications , vol.17 , pp. 37-47
    • Mangasarian, O.L.1    Fromovitz, S.2
  • 12
    • 0002517759 scopus 로고
    • On the Kuhn-Tucker Theorem
    • Edited by J. Abadie, North Holland, Amsterdam, Holland
    • ABADIE, J. M., On the Kuhn-Tucker Theorem, Nonlinear Programming, Edited by J. Abadie, North Holland, Amsterdam, Holland, pp. 19-36, 1967.
    • (1967) Nonlinear Programming , pp. 19-36
    • Abadie, J.M.1
  • 13
    • 4444266928 scopus 로고
    • A Review of Constraint Qualifications in Finite-Dimensional Spaces
    • PETERSON, D. W., A Review of Constraint Qualifications in Finite-Dimensional Spaces, SIAM Review, Vol. 15, pp. 639-654, 1973.
    • (1973) SIAM Review , vol.15 , pp. 639-654
    • Peterson, D.W.1
  • 14
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, New Jersey
    • ROCKAFELLAR, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 15
    • 0013467326 scopus 로고
    • Structural Stability in Nonlinear Optimization
    • GUDDAT, J., JONGEN, H. T., Structural Stability in Nonlinear Optimization, Optimization, Vol. 18, pp. 617-631, 1987.
    • (1987) Optimization , vol.18 , pp. 617-631
    • Guddat, J.1    Jongen, H.T.2
  • 19
    • 0004231786 scopus 로고
    • Oliver and Boyd, Edinburgh, Scotland
    • BERGE, C., Topological Spaces, Oliver and Boyd, Edinburgh, Scotland, 1963.
    • (1963) Topological Spaces
    • Berge, C.1
  • 20
    • 0001683067 scopus 로고
    • Point-to-Set Maps in Mathematical Programming
    • HOGAN, W. W., Point-to-Set Maps in Mathematical Programming, SIAM Review, Vol. 15, pp. 591-603, 1973.
    • (1973) SIAM Review , vol.15 , pp. 591-603
    • Hogan, W.W.1
  • 21
    • 4444383938 scopus 로고
    • Geometry of Optimality Conditions and Constraint Qualifications
    • GOULD, F. J., and TOLLE, J. W., Geometry of Optimality Conditions and Constraint Qualifications, Mathematical Programming, Vol. 2, pp. 1-18, 1972.
    • (1972) Mathematical Programming , vol.2 , pp. 1-18
    • Gould, F.J.1    Tolle, J.W.2
  • 22
    • 0000923543 scopus 로고
    • Generalized Kuhn-Tucker Conditions for Mathematical Programming Problems in a Banach Space
    • GUIGNARD, M., Generalized Kuhn-Tucker Conditions for Mathematical Programming Problems in a Banach Space, SIAM Journal on Control, Vol. 7, pp. 232-241, 1969.
    • (1969) SIAM Journal on Control , vol.7 , pp. 232-241
    • Guignard, M.1
  • 23
    • 0010763969 scopus 로고
    • Geometry of Optimality Conditions and Constraint Qualifications: The Convex Case
    • WOLKOWICZ, H., Geometry of Optimality Conditions and Constraint Qualifications: The Convex Case, Mathematical Programming, Vol. 19, pp. 32-60, 1980.
    • (1980) Mathematical Programming , vol.19 , pp. 32-60
    • Wolkowicz, H.1
  • 24
    • 0035435189 scopus 로고    scopus 로고
    • First-Order Optimality Conditions for Degenerate Index Sets in Generalized Semi-Infinite Programming
    • STEIN, O., First-Order Optimality Conditions for Degenerate Index Sets in Generalized Semi-Infinite Programming, Mathematics of Operations Research, Vol. 26, pp. 565-582, 2001.
    • (2001) Mathematics of Operations Research , vol.26 , pp. 565-582
    • Stein, O.1
  • 27
    • 0002940114 scopus 로고
    • Extremum Problems with Inequalities as Subsidiary Conditions
    • R. Courant Anniversary Volume, Interscience, New York, NY
    • JOHN, F., Extremum Problems with Inequalities as Subsidiary Conditions, Studies and Essays, R. Courant Anniversary Volume, Interscience, New York, NY, pp. 187-204, 1948.
    • (1948) Studies and Essays , pp. 187-204
    • John, F.1
  • 28
    • 0027657329 scopus 로고
    • Semi-Infinite Programming: Theory, Methods and Applications
    • HETTICH, R., and KORTANEK, K. O., Semi-Infinite Programming: Theory, Methods and Applications, SIAM Review, Vol. 35, pp. 380-429, 1993.
    • (1993) SIAM Review , vol.35 , pp. 380-429
    • Hettich, R.1    Kortanek, K.O.2
  • 30
    • 84862411622 scopus 로고    scopus 로고
    • Preprint, Departamento de Física y Matemáticas, Escuela de Ciencias, Universidad de las Américas, Puebla, Mexico
    • GUERRA VASQUEZ, F., and OROZCO, J. A., On Constraint Qualifications in Semi-Infinite Optimization, Preprint, Departamento de Física y Matemáticas, Escuela de Ciencias, Universidad de las Américas, Puebla, Mexico, 2001.
    • (2001) On Constraint Qualifications in Semi-Infinite Optimization
    • Guerra Vasquez, F.1    Orozco, J.A.2
  • 31
    • 4444223776 scopus 로고
    • Nonlinear Programming: A Historical View
    • Edited by R. W. Cottle and C. E. Lemke, American Mathematical Society, Providence, Rhode Island
    • KUHN, H. W., Nonlinear Programming: A Historical View, Nonlinear Programming, Edited by R. W. Cottle and C. E. Lemke, American Mathematical Society, Providence, Rhode Island, pp. 1-26, 1976.
    • (1976) Nonlinear Programming , pp. 1-26
    • Kuhn, H.W.1
  • 32
    • 0019138551 scopus 로고
    • Differential Stability in Infinite-Dimensional Nonlinear Programming
    • LEMPIO, F., and MAURER, H., Differential Stability in Infinite-Dimensional Nonlinear Programming, Applied Mathematics and Optimization, Vol. 6, pp. 139-152, 1980.
    • (1980) Applied Mathematics and Optimization , vol.6 , pp. 139-152
    • Lempio, F.1    Maurer, H.2
  • 33
    • 0026867929 scopus 로고
    • Partially-Finite Convex Programming, Part 1: Duality Theory
    • BORWEIN, J. M., and LEWIS, A. S., Partially-Finite Convex Programming, Part 1: Duality Theory, Mathematical Programming, Vol. 57, pp. 15-48, 1992.
    • (1992) Mathematical Programming , vol.57 , pp. 15-48
    • Borwein, J.M.1    Lewis, A.S.2
  • 34
    • 0026869613 scopus 로고
    • Partially-Finite Convex Programming, Part 2: Explicit Lattice Models
    • BORWEIN, J. M., and LEWIS, A. S., Partially-Finite Convex Programming, Part 2: Explicit Lattice Models, Mathematical Programming, Vol. 57, pp. 49-84, 1992.
    • (1992) Mathematical Programming , vol.57 , pp. 49-84
    • Borwein, J.M.1    Lewis, A.S.2
  • 35
    • 84974399486 scopus 로고
    • Characterization of Optimality for the Abstract Convex Program with Finite-Dimensional Range
    • BORWEIN, J. M., and WOLKOWICZ, H., Characterization of Optimality for the Abstract Convex Program with Finite-Dimensional Range, Journal of the Australian Mathematical Society, Vol. 30A, pp. 390-411, 1980/81.
    • (1980) Journal of the Australian Mathematical Society , vol.30 A , pp. 390-411
    • Borwein, J.M.1    Wolkowicz, H.2
  • 36
    • 0022719721 scopus 로고
    • A Simple Constraint Qualification in Infinite-Dimensional Programming
    • BORWEIN, J. M., and WOLKOWICZ, H., A Simple Constraint Qualification in Infinite-Dimensional Programming, Mathematical Programming, Vol. 35, pp. 83-96, 1986.
    • (1986) Mathematical Programming , vol.35 , pp. 83-96
    • Borwein, J.M.1    Wolkowicz, H.2
  • 37
    • 0020827754 scopus 로고
    • A Duality Theorem for Semi-Infinite Convex Programs and Their Finite Subprograms
    • KARNEY, D. F., A Duality Theorem for Semi-Infinite Convex Programs and Their Finite Subprograms, Mathematical Programming, Vol. 27, pp. 75-82, 1983.
    • (1983) Mathematical Programming , vol.27 , pp. 75-82
    • Karney, D.F.1
  • 38
    • 0034550220 scopus 로고    scopus 로고
    • Constraint Qualifications for Semi-Infinite Systems of Convex Inequalities
    • LI, W., NAHAK, C., and SINGER, I., Constraint Qualifications for Semi-Infinite Systems of Convex Inequalities, SIAM Journal on Optimization, Vol. 11, pp. 31-52, 2000.
    • (2000) SIAM Journal on Optimization , vol.11 , pp. 31-52
    • Li, W.1    Nahak, C.2    Singer, I.3
  • 39
    • 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, Operations Research, Vol. 21, pp. 188-209, 1973.
    • (1973) Operations Research , vol.21 , pp. 188-209
    • Hogan, W.W.1
  • 40
    • 0000437101 scopus 로고    scopus 로고
    • Generalized Semi-Infinite Programming: Numerical Aspects
    • STILL, G., Generalized Semi-Infinite Programming: Numerical Aspects, Optimization, Vol. 49, pp. 223-242, 2001.
    • (2001) Optimization , vol.49 , pp. 223-242
    • Still, G.1
  • 41
    • 0020166920 scopus 로고
    • Differential Properties of the Marginal Function in Mathematical Programming
    • GAUVIN, J., and DUBEAU, F., Differential Properties of the Marginal Function in Mathematical Programming, Mathematical Programming Study, Vol. 19, pp. 101-119, 1982.
    • (1982) Mathematical Programming Study , vol.19 , pp. 101-119
    • Gauvin, J.1    Dubeau, F.2
  • 42
    • 0022076983 scopus 로고
    • On Uniqueness of Kuhn-Tucker Multipliers in Nonlinear Programming
    • KYPARISIS, J., On Uniqueness of Kuhn-Tucker Multipliers in Nonlinear Programming, Mathematical Programming, Vol. 32, pp. 242-246, 1985.
    • (1985) Mathematical Programming , vol.32 , pp. 242-246
    • Kyparisis, J.1
  • 43
    • 0021449289 scopus 로고
    • Some Examples and Counterexamples for the Stability Analysis of Nonlinear Programming Problems
    • GAUVIN, J., and DUBEAU, F., Some Examples and Counterexamples for the Stability Analysis of Nonlinear Programming Problems, Mathematical Programming Study, Vol. 21, pp. 69-78, 1983.
    • (1983) Mathematical Programming Study , vol.21 , pp. 69-78
    • Gauvin, J.1    Dubeau, F.2
  • 45
    • 0034348927 scopus 로고    scopus 로고
    • On Optimality Conditions for Generalized Semi-Infinite Programming Problems
    • STEIN, O., and STILL, G., On Optimality Conditions for Generalized Semi-Infinite Programming Problems, Journal of Optimization Theory and Applications, Vol. 104, pp. 443-458, 2000.
    • (2000) Journal of Optimization Theory and Applications , vol.104 , pp. 443-458
    • Stein, O.1    Still, G.2
  • 46
    • 4444329329 scopus 로고    scopus 로고
    • Structural Stability in Generalized Semi-Infinite Optimization
    • WEBER, G. W., Structural Stability in Generalized Semi-Infinite Optimization, Vychislitel'nye Tekhnologii, Vol. 6, pp. 25-46, 2001.
    • (2001) Vychislitel'nye Tekhnologii , vol.6 , pp. 25-46
    • Weber, G.W.1
  • 47
    • 0033239456 scopus 로고    scopus 로고
    • First-Order Optimality Conditions in Generalized Semi-Infinite Programming
    • RÜCKMANN, J. J., and SHAPIRO, A., First-Order Optimality Conditions in Generalized Semi-Infinite Programming, Journal of Optimization Theory and Applications, Vol. 101, pp. 677-691, 1999.
    • (1999) Journal of Optimization Theory and Applications , vol.101 , pp. 677-691
    • Rückmann, J.J.1    Shapiro, A.2
  • 48
    • 0000016156 scopus 로고    scopus 로고
    • Generalized Semi-Infinite Optimization: A First Order Optimality Condition and Examples
    • JONGEN, H. T., RÜCKMANN, J. J., and STEIN, O., Generalized Semi-Infinite Optimization: A First Order Optimality Condition and Examples, Mathematical Programming, Vol. 83, pp. 145-158, 1998.
    • (1998) Mathematical Programming , vol.83 , pp. 145-158
    • Jongen, H.T.1    Rückmann, J.J.2    Stein, O.3


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