Mangasarian, O. L.,Sparsity-Preserving SOR Algorithms for Separable Quadratic and Linear Programming, Computers and Operations Research, Vol. 11, pp. 105–112, 1984.
Mangasarian, O. L., andDe Leone, R.,Parallel Gradient Projection Successive Overrelaxation for Symmetric Linear Complementarity Problems and Linear Programs, Annals of Operations Research, Vol. 14, pp. 41–59, 1988.
Herman, G. T., andLent, A.,A Family of Iterative Quadratic Optimization Algorithms for Pairs of Inequalities, with Application in Diagnostic Radiology, Mathematical Programming Study, Vol. 9, pp. 15–29, 1978.
Cottle, R. W., andGoheen, M. S.,A Special Class of Large Quadratic Programs, Nonlinear Programming 3, Edited by O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, Academic Press, New York, New York, pp. 361–390, 1978.
Cottle, R. W., Golub, G. H., andSacher, R. S.,On the Solution of Large, Structured Linear Complementarity Problems: The Block-Partitioned Case, Applied Mathematics and Optimization, Vol. 4, pp. 347–363, 1978.
Dembo, R. S., andTulowitzki, U.,On the Minimization of Quadratic Functions Subject to Box Constraints, Yale University, School of Organization and Management, Working Paper Series B, No. 78, 1983; revised 1984.
Arimoto, S.,An Algorithm for Computing the Capacity of Arbitrary DMCs, IEEE Transactions on Information Theory, Vol. IT-18, pp. 14–20, 1972.
Blahut, R.,Computation of Channel Capacity and Rate Distortion Functions, IEEE Transactions on Information Theory, Vol. IT-18, pp. 460–473, 1972.
Kruithof, J.,Calculation of Telephone Traffic, De Ingenieur (E. Electrotechnik 3), Vol. 52, pp. E15–25, 1937.
Lamond, B., andStewart, N. F.,Bregman's Balancing Method, Transportation Research, Vol. 15B, pp. 239–248, 1981.
Censor, Y.,Parallel Application of Block-Iterative Methods in Medical Imaging and Radiation Therapy, Mathematical Programming, Series B, Vol. 42, pp. 307–325, 1988.
Lent, A.,A Convergent Algorithm for Maximum Entropy Image Restoration with a Medical X-Ray Application, Image Analysis and Evaluation, Edited by R. Shaw, Society of Photographic Scientists and Engineers, Washington, DC, pp. 249–257, 1977.
Powell, M. J. D.,An Algorithm for Maximizing Entropy Subject to Simple Bounds, Mathematical Programming, Vol. 42, pp. 171–180, 1988.
Frieden, B. R.,Image Enhancement and Restoration, Picture Processing and Digital Filtering, Edited by T. S. Huang, Springer-Verlag, Berlin, Germany, pp. 177–248, 1975.
Jaynes, E. T.,On the Rationale of Maximum Entropy Methods, Proceedings of the IEEE, Vol. 70, pp. 939–952, 1982.
Johnson, R., andShore, J. E.,Which Is the Better Entropy Expression for Speech Processing—S log S or log S?, IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-32, pp. 129–136, 1984.
Darroch, J. N., andRatcliff, D.,Generalized Iterative Scaling for Log-Linear Models, Annals of Mathematical Statistics, Vol. 43, pp. 1470–1480, 1972.
Freund, R. M.,Projective Transformations for Interior Point Methods, Part 1: Basic Theory and Linear Programming, Massachusetts Institute of Technology, Operations Research Center, Working Paper No. 180–88, 1988.
Huard, P.,Resolution of Mathematical Programming with Nonlinear Constraints by the Method of Centers, Nonlinear Programming, Edited by J. Abadie, North-Holland, Amsterdam, Holland, pp. 207–219, 1967.
Karmarkar, N.,A New Polynomial-Time Algorithm for Linear Programming, Combinatorica, Vol. 4, pp. 373–395, 1984.
Sonnevend, G.,New Algorithms in Convex Programming Based on a Notion of Center for Systems of Analytic Inequalities and on Rational Extrapolation, Trends in Mathematical Optimization, Edited by K. H. Hoffman, J. B. Hiriart-Urruty, J. Zowe, and C. Lemarechal, Birkhäuser-Verlag, Basel, Switzerland, pp. 311–326, 1988.
Hildreth, C.,A Quadratic Programming Procedure, Naval Research Logistics Quarterly, Vol. 4, pp. 79–85, 1957; see alsoErratum, Vol. 4, p. 361, 1957.
Cottle, R. W., andPang, J.-S.,On the Convergence of a Block Successive Overrelaxation Method for a Class of Linear Complementarity Problems, Mathematical Programming Study, Vol. 17, pp. 126–138, 1982.
Cryer, C. W.,The Solution of a Quadratic Programming Problem Using Systematic Overrelaxation, SIAM Journal on Control and Optimization, Vol. 9, pp. 385–392, 1971.
Bachem, A., andKorte, B.,On the RAS Algorithm, Computing, Vol. 23, pp. 189–198, 1979.
Bregman, L. M.,Proof of the Convergence of Sheleikhovskii's Method for a Problem with Transportation Constraints, USSR Computational Mathematics and Mathematical Physics, Vol. 1, pp. 191–204, 1967.
Schneider, M. H., andZenios, S. A.,A Comparative Study of Algorithms for Matrix Balancing, Operations Research, Vol. 38, pp. 439–455, 1990.
Zenios, S. A., andIu, S. L.,Vector and Parallel Computing for Matrix Balancing, Annals of Operations Research, Vol. 22, pp. 161–180, 1990.
Censor, Y., andLent, A.,Optimization of log x Entropy over Linear Equality Constraints, SIAM Journal on Control and Optimization, Vol. 25, pp. 921–933, 1987.
Auslender, A.,Optimisation: Méthodes Numériques, Masson, Paris, France, 1976.
Bertsekas, D. P., andTsitsiklis, J. N.,Parallel and Distributed Computation: Numerical Methods, Prentice-Hall, Englewood Cliffs, New Jersey, 1989.
D'esopo, D. A.,A Convex Programming Procedure, Naval Research Logistics Quarterly, Vol. 6, pp. 33–42, 1959.
Glowinski, R.,Numerical Methods for Nonlinear Variational Problems, Springer-Verlag, New York, New York, 1984.
Luenberger, D. G.,Linear and Nonlinear Programming, Addison-Wesley, Reading, Massachusetts, 1973.
Polak, E.,Computational Methods in Optimization: A Unified Approach, Academic Press, New York, New York, 1971.
Powell, M. J. D.,On Search Directions for Minimization Algorithms, Mathematical Programming, Vol. 4, pp. 193–201, 1973.
Sargent, R. W. H., andSebastian, D. J.,On the Convergence of Sequential Minimization Algorithms, Journal of Optimization Theory and Applications, Vol. 12, pp. 567–575, 1973.
Zangwill, W. I.,Nonlinear Programming: A Unified Approach, Prentice-Hall, Englewood Cliffs, New Jersey, 1969.
Tseng, P.,Dual Ascent Methods for Problems with Strictly Convex Costs and Linear Constraints: A Unified Approach, SIAM Journal on Control and Optimization, Vol. 28, pp. 214–242, 1990.
Tseng, P.,Descent Methods for Convex Essentially Smooth Optimization, Journal of Optimization Theory and Applications, Vol. 70, pp. 109–135, 1991.
Tseng, P., andBertsekas, D. P.,Relaxation Methods for Problems with Strictly Convex Costs and Linear Constraints, Mathematics of Operations Research, Vol. 16, pp. 462–481, 1991.
Bregman, L. M.,The Relaxation Method of Finding the Common Point Convex Sets and Its Application to the Solution of Problems in Convex Programming, USSR Computational Mathematics and Mathematical Physics, Vol. 7, pp. 200–217, 1967.
Pang, J. S.,On the Convergence of Dual Ascent Methods for Large-Scale Linearly Constrained Optimization, University of Texas at Dallas, School of Management, Technical Report, 1984.
Bertsekas, D. P., Hosein, P. A., andTseng, P.,Relaxation Methods for Newtork flow Problems with Convex Arc Costs, SIAM Journal on Control and Optimization, Vol. 25, pp. 1219–1243, 1987.
Luo, Z. Q., andTseng, P.,On the Convergence of a Matrix-Splitting Algorithm for the Symmetric Monotone Linear Complementarity Problem, SIAM Journal on Control and Optimization, Vol. 29, pp. 1037–1060, 1991.
Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
Ortega, J. M., andRheinboldt, W. C.,Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, New York, 1970.
Tseng, P., andBertsekas, D. P.,Relaxation Methods for Problems with Strictly Convex Separable Costs and Linear Constraints, Mathematical Programming, Vol. 38, pp. 303–321, 1987.
Hoffman, A. J.,On Approximate Solutions of Systems of Linear Inequalities, Journal of Research of the National Bureau of Standards, Vol. 49, pp. 263–265, 1952.
Robinson, S. M.,Bounds for Errors in the Solution Set of a Perturbed Linear Program, Linear Algebra and Its Applications, Vol. 6, pp. 69–81, 1973.
Mangasarian, O. L., andShiau, T. H.,Lipschitz Continuity of Solutions of Linear Inequalities: Programs and Complementarity Problems, SIAM Journal on Control and Optimization, Vol. 25, pp. 583–595, 1987.
Luo, Z. Q., andTseng, P.,On the Linear Convergence of Descent Methods for Convex Essentially Smooth Minimization, SIAM Journal on Control and Optimization (to appear).
Lin, Y. Y., andPang, J. S.,Iterative Methods for Large Convex Quadratic Programs: A Survey, SIAM Journal on Control and Optimization, Vol. 18, pp. 383–411, 1987.
Iusem, A. N., andDe Pierro, A. R.,On the Convergence Properties of Hildreth's Quadratic Programming Algorithm, Mathematical Programming, Series A, Vol. 47, pp. 37–51, 1990.
De Pierro, A. R., andIusem, A. N.,A Relaxed Version of Bregman's Method for Convex Programming, Journal of Optimization Theory and Applications, Vol. 51, pp. 421–440, 1986.
Censor, Y., andLent, A.,An Iterative Row-Action Method for Interval Convex Programming, Journal of Optimization Theory and Applications, Vol. 34, pp. 321–352, 1981.