Olvi L. Mangasarian

John von Neumann Professor of Mathematics and Computer Sciences, and member of the Center for the Mathematical Sciences

Computer Sciences Department
University of Wisconsin
1210 W. Dayton St.
Madison, WI 53706-1685

Telephone: (608) 262-1204
Fax: (608) 262-9777
Email: olvi@cs.wisc.edu
Ph.D., Harvard University, 1959
Interests: Mathematical programming, machine learning, and parallel computing


Research Summary

Optimization theory is rich mathematically while being very effective computationally in solving many real-life problems. My interests in this topic have ranged over a broad spectrum that encompasses theoretical aspects, such as error bounds for mathematical programs and variational inequalities, convergence proofs for parallel gradient and variable distribution algorithms for optimization, smoothing techniques for solving constrained optimization problems as differentiable nonlinear equations, as well as applications to machine learning, both in general and specific contexts. An important aspect of my research is the use of mathematical programming techniques in diagnosing breast cancer, that has resulted in a highly accurate computerized diagnostic system in current use at University of Wisconsin Hospitals.


Current PhD Students

  • Paul Bradley

  • Recent Publications

    O. L. Mangasarian and M. V. Solodov
    A Linearly Convergent Descent Method for Strongly Monotone Complementarity Problems.
    Mathematical Programming Technical Report 96-07, October 1996.
    O. L. Mangasarian and Jong-Shi Pang
    Exact Penalty Functions for Mathematical Programs with Linear Complementarity Constraints.
    Mathematical Programming Technical Report 96-06, August 1996.
    O. L. Mangasarian
    Mathematical Programming in Data Mining
    Mathematical Programming Technical Report 96-05, August 1996.
    O. L. Mangasarian
    Error Bounds for Nondifferentiable Convex Inequalities under a Strong S later Constraint Qualification.
    Mathematical Programming Technical Report 96-04, July 1996.
    P. S. Bradley, O. L. Mangasarian and W. N. Street
    Clustering via Concave Minimization.
    Mathematical Programming Technical Report 96-03, May 1996. Submitted to Neural Information Processing Systems 1996.
    W. N. Street, O. L. Mangasarian and W. H. Wolberg
    Individual and Collective Prognostic Prediction.
    Mathematical Programming Technical Report 96-01, January 1996.
    P. S. Bradley, O. L. Mangasarian and W. N. Street
    Feature Selection via Mathematical Programming.
    Mathematical Programming Technical Report 95-21, December 1995. Submitted to INFORMS Journal on Computing.
    O. L. Mangasarian
    Machine Learning via Polyhedral Concave Minimization.
    Mathematical Programming Technical Report 95-20, November 1995. "Applied Mathematics and Parallel Computing -- Festschrift for Klaus Ritter", H. Fischer, B. Riedmueller, S. Schaeffler, editors, Physica-Verlag, Germany 1996, 175-188.
    O. L. Mangasarian
    The Ill-Posed Linear Complementarity Problem.
    Mathematical Programming Technical Report 95-15, August 1995. Submitted to SIAM Proceedings of the International Symposium on Complementarity Problems, Baltimore, MD, November 1-4, 1995. Revised November 1995.
    W. Nick Street and O. L. Mangasarian
    Improved Generalization via Tolerant Training.
    Mathematical Programming Technical Report 95-11, July 1995.
    O. L. Mangasarian
    Mathematical Programming in Machine Learning.
    Mathematical Programming Technical Report 95-06, April 1995, Revised July 1995. To appear in Proceedings of Nonlinear Optimization and Applications Workshop, Erice June 1995, Plenum Press.
    Chunhui Chen and O. L. Mangasarian
    Hybrid Misclassification Minimization.
    Mathematical Programming Technical Report 95-05, February 1995, Revised July 1995 and August 1995. To appear in Advances in Computational Mathematics.
    O. L. Mangasarian
    Optimization in Machine Learning.
    Mathematical Programming Technical Report 95-01, January 1995. SIAG/OPT Views-and-News 6, 1995, 3-7.
    Chunhui Chen and O. L. Mangasarian
    A Class of Smoothing Functions for Nonlinear and Mixed Complementarity Problems.
    Mathematical Programming Technical Report 94-11, August 1994. Revised October 1994, February 1995 and September 1995. Computational Optimization and Applications 5, 1996, 97-138.
    O. L. Mangasarian, W. Nick Street and W. H. Wolberg
    Breast Cancer Diagnosis and Prognosis via Linear Programming.
    Mathematical Programming Technical Report 94-10, August 1994. Revised December 1994. Operations Research 43(4), July-August 1995, 570-577.
    O. L. Mangasarian
    The Linear Complementarity Problem as a Separable Bilinear Program.
    Mathematical Programming Technical Report 94-09, July 1994. Journal of Global Optimization 6, 1995, 153-161.
    O. L. Mangasarian and M. V. Solodov
    Backpropagation Convergence via Deterministic Nonmonotone Perturbed Minimization.
    Mathematical Programming Technical Report 94-06, June 1994. Advances in Neural Information Processing Systems 6, (J. D. Cowan, G. Tesauro and J. Alspector, editors) 383-390, Morgan Kaufmann Publishers, San Francisco, California 1994.
    Chunhui Chen and O. L. Mangasarian
    Smoothing Methods for Convex Inequalities and Linear Complementarity Problems.
    Computer Sciences Technical Report 1191r, November 1993. Revised November 1994. Mathematical Programming 71, 1995, 51-69.
    O. L. Mangasarian
    Misclassification Minimization.
    Computer Sciences Technical Report 1186, October 1993. Revised September 1994. Journal of Global Optimization 5(4), December 1994, 309-323.
    O. L. Mangasarian and M. V. Solodov
    Serial and Parallel Backpropagation for Neural Nets via Nonmonotone Perturbed Minimnization.
    Computer Sciences Technical Report 1149r, April 1993. Revised December 1993. Optimization Methods and Software 4, 1994, 103-116.

    Chronological cancer bibliography

    WWW Page of Other Publications of MP Group at Wisconsin

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    periodically updated by olvi@cs.wisc.edu