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Locally unique solutions of quadratic programs, linear and nonlinear complementarity problems.(English)Zbl 0442.90089


MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C20 Quadratic programming

Cite

References:

[1]R.W. Cottle, ”Nonlinear programs with positively bounded Jacobians”,SIAM Journal on Applied Mathematics 14 (1966) 147–158. ·Zbl 0158.18903 ·doi:10.1137/0114012
[2]R.W. Cottle and G.B. Dantzig, ”Complementary pivot theory of mathematical programming”,Linear Algebra and Its Applications 1 (1968) 103–125. ·Zbl 0155.28403 ·doi:10.1016/0024-3795(68)90052-9
[3]A.V. Fiacco and G.P. McCormick,Nonlinear programming: sequential unconstrained minimization techniques (Wiley, New York, 1968). ·Zbl 0193.18805
[4]I. Kaneko, ”The number of solutions of a class of linear complementarity problems”,Mathematical Programming 17 (1979) 104–105. ·Zbl 0407.90082 ·doi:10.1007/BF01588229
[5]S. Karamardian, ”The nonlinear complementarity problem with applications I and II”,Journal of Optimization Theory and Applications 4 (1969) 87–98 and 167–181. ·Zbl 0169.06901 ·doi:10.1007/BF00927414
[6]W. Karush, ”Minima of functions of several variables with inequalities as side conditions”, Master of Science Dissertation, Department of Mathematics, University of Chicago (Chicago, IL, December 1939).
[7]M. Kojima, ”Studies on piecewise-linear approximations of piecewise–C 1 mappings in fixed points and complementarity theory”,Mathematics of Operations Research 3 (1978) 17–36. ·Zbl 0396.41012 ·doi:10.1287/moor.3.1.17
[8]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
[9]A. Majthay, ”Optimality conditions for quadratic programming”,Mathematical Programming 1 (1971) 359–365. ·Zbl 0246.90038 ·doi:10.1007/BF01584097
[10]O.L. Mangasarian, Nonlinear programming (McGraw-Hill, New York, 1969). ·Zbl 0194.20201
[11]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
[12]O.L. Mangasarian, ”Equivalence of the complementarity problem to a system of nonlinear equations”,SIAM Journal on Applied Mathematics 31 (1976) 89–92. ·Zbl 0339.90051 ·doi:10.1137/0131009
[13]N. Megiddo and M. Kojima, ”On the existence and uniqueness of solutions in nonlinear complementarity theory”,Mathematical Programming 12 (1977) 110–130. ·Zbl 0363.90102 ·doi:10.1007/BF01593774
[14]J.J. Moré, ”Coercivity conditions in nonlinear complementarity problems”,SIAM Review 16 (1974) 1–15. ·doi:10.1137/1016001
[15]J.J. Moré, ”Classes of functions and feasibility conditions in nonlinear complementarity problems”,Mathematical Programming 6 (1974) 327–338. ·Zbl 0291.90059 ·doi:10.1007/BF01580248
[16]K.G. Murty, ”On the number of solutions to the complementarity problem and spanning properties of complementary cones”,Linear Algebra and Its Applications 5 (1972) 65–108. ·Zbl 0241.90046 ·doi:10.1016/0024-3795(72)90019-5
[17]S.M. Robinson, ”Strongly regular generalized equations”, University of Wisconsin, Mathematics Research Center Technical Report No. 1877 (September 1978) forthcoming inMathematics of Operations Research.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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