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Ben-Tal, A.

Second-order and related extremality conditions in nonlinear programming. (English) Zbl 0416.90062

J. Optimization Theory Appl. 31, 143-165 (1980).
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Cited in 2 Reviews
Cited in 91 Documents

MSC:

90C30 Nonlinear programming

Keywords:

nonlinear programming; local minimum; equality and inequality constraints; second-order conditions; curvature information; conditions of Fritz-John-type
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Full Text: DOI

References:

[1] Mangasarian, O. L., andFromovitz, S. The Fritz John Necessary Optimality Conditions in the Presence of Equality and Inequality Constraints, Journal of Mathematical Analysis and Applications, Vol. 17, pp. 73-74, 1967. · Zbl 0149.16701 · doi:10.1016/0022-247X(67)90163-1
[2] John, F.,Extremum Problem with Inequalities as Subsidiary Conditions, Studies and Essays: Courant Anniversary Volume, Edited by K. O. Friedrichs, O.E. Neugebauer, and J. J. Stoker, John Wiley and Sons, New York, New York, 1948.
[3] McShane, E. J.,Sufficient Conditions for a Weak Relative Minimum in the Problem of Bolza, Transactions of American Mathematical Society, Vol. 52, pp. 344-379, 1942. · Zbl 0063.03871 · doi:10.1090/S0002-9947-1942-0006828-2
[4] Fiacco, A. V., andMcCormick, G. P.,Nonlinear Programming: Sequential Unconstrained Minimization Techniques, John Wiley and Sons, New York, New York, 1968. · Zbl 0193.18805
[5] Penissi, E. J.,An Indirect Sufficiency Proof for the Problem of Lagrange with Differential Inequalities as Added Side Conditions, Transactions of American Mathematical Society, Vol. 74, pp. 177-198, 1953. · Zbl 0050.32602 · doi:10.1090/S0002-9947-1953-0052706-X
[6] McCormick, G. P.,Second-Order Conditions for Constrained Minima, SIAM Journal on Applied Mathematics, Vol. 15, pp. 641-652, 1967. · Zbl 0166.15601 · doi:10.1137/0115056
[7] Luenberger, D. E.,Introduction to Linear and Nonlinear Programming, Addison-Wesley Publishing Company, Reading, Massachusetts, 1973. · Zbl 0297.90044
[8] Avriel, M.,Nonlinear Programming, Analysis and Methods, Prentice Hall, Englewood Cliffs, New Jersey, 1976. · Zbl 0361.90035
[9] Collatz, L., andWetterling, W.,Optimization Problems, Springer-Verlag, New York, New York, 1975. · Zbl 0365.90001
[10] Mangasarian, O. L.,Nonlinear Programming, McGraw-Hill Book Company, New York, New York, 1969.
[11] Ben-Tal, A., Ben-Israel, A., andZlobec, S.,Characterization of Optimality in Convex Programming without a Constraint Qualification, Journal of Optimization Theory and Applications, Vol. 20, pp. 417-437, 1976. · Zbl 0327.90025 · doi:10.1007/BF00933129
[12] Hestenes, M. R.,Optimization Theory, The Finite Dimensional Case, John Wiley and Sons, New York, New York, 1975. · Zbl 0327.90015
[13] Fan, K. On System of Linear Inequalities, Linear Inequalities and Related Systems, Edited by H. W. Kuhn and A. W. Tucker, Princeton University Press, Princeton, New Jersey, 1956. · Zbl 0072.37602
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