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Iterative methods for linear complementarity problems with upperbounds on primary variables.(English)Zbl 0506.90081


MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C20 Quadratic programming
91B50 General equilibrium theory

Cite

References:

[1]M. Aganagic, ”Variational inequalities and generalized complementaritys problems”, Technical Report 78-11, Department of Operations Research, Stanford University (Stanford, CA, September 1978).
[2]Byong-hun Ahn and W. W. Hogan, ”On convergence of the PIES algorithm for computing equilibria”,Operations Research 30 (1982) 281–300 ·Zbl 0481.90011 ·doi:10.1287/opre.30.2.281
[3]Byong-hun Ahn, ”Solution of nonsymmetric linear complementarity problems by iterative methods”,Journal of Optimization Theory and Applications 33 (1981) 175–185 ·Zbl 0422.90079 ·doi:10.1007/BF00935545
[4]R. Chandrasekaran, ”A special case of the complementary pivot problem”,Opsearch 7 (1970) 263–268
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[7]R.W. Cottle and M. Goheen, ”A special class of large quadratic programs”, in: O.L. Mangasarian, R.R. Meyer and S.M. Robinson, eds,Nonlinear programming 3 (Academic Press, New York, 1978) pp. 361–390. ·Zbl 0458.90049
[8]R.W. Cottle, G. Golub, and R.S. Sacher, ”On the solution of large structured linear complementarity problems”,Applied Mathematics and Optimization 4 (1978) 347–363 ·Zbl 0391.90087
[9]C.W. Cryer, ”The solution of quadratic programming problems using systematic overrelaxation”,SIAM Journal on Control 9 (1971) 385–392. ·Zbl 0216.54603 ·doi:10.1137/0309028
[10]S. Dafermos, ”Traffic equilibrium and variational inequalities”,Transportation Science 14 (1980) 52–54. ·doi:10.1287/trsc.14.1.42
[11]M.A. Diamond, ”The solution of a quadratic programming problem using fast methods to solve systems of linear equations”,International Journal of Systems Science 5 (1974) 131–136. ·Zbl 0297.90065 ·doi:10.1080/00207727408920083
[12]M. Fiedler and V. Pták, ”On matrices with nonpositive off-diagonal elements and positive principal minors”,Czechoslovak Mathematical Journal 12 (1962) 382–400. ·Zbl 0131.24806
[13]R. Fletcher and M.P. Jackson, ”Minimization of a quadratic function of many variables subject only to lower and upper bounds”,Journal of Institute for Mathematics and Its Applications 14 (1974) 159–174. ·Zbl 0301.90032 ·doi:10.1093/imamat/14.2.159
[14]T. Hansen and A.S. Manne, ”Equilibrium and linear complementarity–an economy with institutional constraints on prices”, in: G. Schwödiauer, ed.,Equilibrium and disequilibrium in economic theory (D. Reidel Publishing Company, Dordrecht, 1977) pp. 227–237.
[15]J.M. Henderson and R.E. Quandt,Microeconomic theory: mathematical approach, 3rd edn. (McGraw-Hill Inc., New York, 1980) pp. 235–264.
[16]W.W. Hogan, ”Project independence evaluation system: structure and algorithm”,Proceedings of Symposia in Applied Mathematics 21 (1977). ·Zbl 0355.90074
[17]L. Hurwicz, ”On the problem of the integrability of demand functions”, in J.C. Chipman, ed.,Preferences, utility and demand (Harcourt Brace Javonovich, New York, 1971). ·Zbl 0294.90007
[18]I. Kaneko, ”Isotone solutions of parametric linear complementarity problems”,Mathematical Programming 12 (1977) 48–59. ·Zbl 0367.90105 ·doi:10.1007/BF01593768
[19]S. Karamardian, ”Generalized complementarity problem”,Journal of Optimization Theory and Applications 8 (1971) 161–168. ·doi:10.1007/BF00932464
[20]O.L. Mangasarian, ”Solution of symmetric linear complementarity problems by iterative methods”,Journal of Optimization Theory and Applications 22 (1977) 465–485. ·Zbl 0341.65049 ·doi:10.1007/BF01268170
[21]L. Mathiesen, ”Efficiency pricing in a linear programming model: a case of constraints on the dual variables,”, Operations Research Report 74-108, Department of Operations Research, Stanford University (Stanford, CA, 1974).
[22]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
[23]A.M. Ostrowski,Solution of equations and systems of equations 2nd edn. (Academic Press, New York, 1966). ·Zbl 0222.65070
[24]J.S. Pang, ”On a class of least-element complementarity problems”,Mathematical Programming 16 (1979) 111–126. ·Zbl 0393.90092 ·doi:10.1007/BF01582097
[25]J.S. Pang, ”The implicit complementarity problem: part II”, Management Science Research Report 459, Graduate School of Industrial Administration, Carnegie-Mellon University (Pittsburgh, PA, 1980).
[26]J. Quirk and R. Saposnik,Introduction to general equilibrium theory and welfare economics (McGraw-Hill, New York, 1968) pp. 61–64.
[27]F. Scarpini, ”Some algorithms solving the unilateral Dirichlet problem with two constraints”,Calcolo 12 (1975) 113–149. ·Zbl 0334.49004 ·doi:10.1007/BF02576012
[28]G. Stampacchia, ”Variational inequalities”, in: A. Ghizzetti, ed.,Theory and application of monotone operators, Proceedings of NATO Advanced Study Institute (Venice, Italy, 1968).
[29]A. Tamir, ”The complementarity problem of mathematical programming”, Ph.D. Thesis, Department of Operations Research, Case Western Reserve University (Cleveland, OH, 1973). ·Zbl 0277.15008
[30]A.F. Veinott Jr, ”Leastd-majorized network flows with inventory and statistical applications”,Management Science 17 (1971) 547–567. ·Zbl 0239.90014 ·doi:10.1287/mnsc.17.9.547
[31]A. Whinston, ”The bounded variable problem–an application of the dual method for quadratic programming”,Naval Research Logistics Quarterly 12 (1975), 173–179. ·Zbl 0133.42802 ·doi:10.1002/nav.3800120205
[32]Y. Yoo, ”Iterative methods for linear complementarity problems and large scale quadratic programming problems”, M. S. Thesis Korea Advanced Institute of Science and Technology (Seoul, Korea, 1981).
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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