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Exact penalty functions in nonlinear programming. (English) Zbl 0424.90057

MSC:
90C30 Nonlinear programming
90C25 Convex programming
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[1] D.P. Bertsekas, ”Necessary and sufficient conditions for a penalty method to be exact”,Mathematical Programming 9 (1975) 87–99. · Zbl 0325.90055 · doi:10.1007/BF01681332
[2] C. Charalambous, ”A lower bound for the controlling parameters of the exact penalty functions”,Mathematical Programming 15 (1978) 278–290. · Zbl 0395.90071 · doi:10.1007/BF01609033
[3] S. Dolecki and S. Rolewicz, ”Exact penalty for local minima”,SIAM Journal on Control and Optimization 17 (1979). · Zbl 0418.90086
[4] J.P. Evans, F.J. Gould and J.W. Tolle, ”Exact penalty functions in nonlinear programming”,Mathematical Programming 4 (1973) 72–97. · Zbl 0267.90079 · doi:10.1007/BF01584647
[5] A.V. Fiacco and G.P. McCormick,Nonlinear programming: sequential unconstrained minimization techniques (Wiley, New York, 1968). · Zbl 0193.18805
[6] U.M. Garcia Palomeres and O.L. Mangasarian, ”Superlinearly convergent quasi-Newton algorithms for nonlinearly constrained optimization problems”,Mathematical Programming 11 (1976) 1–13. · Zbl 0362.90103 · doi:10.1007/BF01580366
[7] S.-P. Han, ”Superlinearly convergent variable metric algorithms for general nonlinear programming problems”,Mathematical Programming 11 (1976) 263–282. · Zbl 0364.90097 · doi:10.1007/BF01580395
[8] S.-P. Han, ”A global convergent method for nonlinear programming”,Journal of Optimization Theory and Applications 22 (1977) 297–309. · Zbl 0336.90046 · doi:10.1007/BF00932858
[9] A.S. Householder,The theory of matrices in numerical analyais (Blaisdell, New York, 1964). · Zbl 0161.12101
[10] S.P. Howe, ”New conditions for exactness of a simple penalty function”,SIAM Journal on Control 11 (1973) 378–381. · Zbl 0255.90054 · doi:10.1137/0311029
[11] W. Karush, ”Minima of functions of several variables with inequalities as side conditions”, Master of Science Dissertation, Department of Mathematics, University of Chicago (Chicago, December 1939).
[12] G.P. McCormick, ”Second order conditions for constrained minima”,SIAM Journal on Applied Mathematics 15 (1967) 641–652. · Zbl 0166.15601 · doi:10.1137/0115056
[13] O.L. Mangasarian,Nonlinear programming (McGraw-Hill, New York, 1969). · Zbl 0194.20201
[14] O.L. Mangasarian, ”Nonlinear programming theory and computation”, in: J.J. Modor and S.E. Elmaghraby, eds.,Handbook of Operations Research (Van Nostrand Reinhold, New York, 1978), pp. 245–265.
[15] O.L. Mangasarian, ”Uniqueness of solution in linear programming”,Linear Algebra and its Applications 25 (1979) 151–162. · Zbl 0399.90053 · doi:10.1016/0024-3795(79)90014-4
[16] O.L. Mangasarian and S. Fromovitz, ”The Fritz John necessary optimality conditions in the presence of equality constraints”,Journal of Mathematical Analysis and Applications 17 (1967) 34–47. · Zbl 0149.16701 · doi:10.1016/0022-247X(67)90163-1
[17] T. Pietrzykowski, ”An exact potential method for constrained maxima”,SIAM Journal on Numerical Analysis 6 (1969) 299–304. · Zbl 0181.46501 · doi:10.1137/0706028
[18] T. Pietrzykowski, ”The potential method for conditioeenal maxima in the locally compact metric spaces”,Numerische Mathematik 14 (1970) 325–329. · Zbl 0195.46304 · doi:10.1007/BF02165588
[19] M.J.D. Powell, ”The convergence of variable metric methods for nonlinearly constrained optimization calculations” in: O.L. Mangasarian, R.R. Meyer and S.M. Robinson, eds.,Nonlinear programming 3 (Academic Press, New York, 1978) pp. 27–64. · Zbl 0464.65042
[20] S.M. Robinson, ”Stability theory for systems of inequalities, part II: Differentiable nonlinear systems”,SIAM Journal on Numerical Analysis 13 (1976) 497–513. · Zbl 0347.90050 · doi:10.1137/0713043
[21] R.T. Rockafellar,Convex analysis (Princeton University Press, Princeton, N.J. 1970). · Zbl 0193.18401
[22] K. Truemper, ”Note on finite convergence of exterior penalty functions”,Management Science 21 (1975) 600–606. · Zbl 0311.90064 · doi:10.1287/mnsc.21.5.600
[23] W.I. Zangwill, ”Nonlinear programming via penalty functions”,Management Science 13 (1967) 344–358. · Zbl 0171.18202 · doi:10.1287/mnsc.13.5.344
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