Michael V. Solodov

Instituto de Matematica Pura e Aplicada
Estrada Dona Castorina 110
Jardim Botanico
Rio de Janeiro
RJ, CEP 22460-320, Brazil

Tel: (55-21) 529-5228
Fax: (55-21) 512-4115
E-mail: solodov@impa.br , solodov@cs.wisc.edu
Web : http://www.cs.wisc.edu/~solodov/solodov.html

PhD Computer Sciences, University of Wisconsin - Madison, 1995.
(advisor Olvi L. Mangasarian ,
John von Neumann Professor of Mathematics and Computer Sciences)
MS Computer Sciences, University of Wisconsin - Madison, 1992.
Diploma with Distinction
Applied Mathematics and Cybernetics, Moscow State University, 1991.

Optimization in Neural Networks

One of the areas of my research has to do with applications of optimization theory and algorithms to problems arising in the neural networks field of artificial intelligence. Neural networks is a large interdisciplinary area of research and it has already found applications in many branches of science and technology. However, much of the work in the area has been based on heuristic concepts and trial-and-error experimentation. It is therefore of great importance to provide rigorous mathematical foundation to neural networks theory and algorithms (where ever possible). I also feel that new more effective machine learning methods can be developed by applying general optimization techniques in conjunction with artificial intelligence paradigms, and by taking advantage of the problem structure. The following papers contain some of the work in this direction.

Relevant Publications

M.V. Solodov: Incremental gradient algorithms with stepsizes bounded away from zero.
Computational Optimization and Applications 11 (1998), 23-35.
O.L. Mangasarian and M.V. Solodov: Serial and Parallel Backpropagation Convergence Via Nonmonotone Perturbed Minimization.
Optimization Methods and Software 4 (1994), 103-116.
M.V. Solodov and S.K. Zavriev: Error stability properties of generalized gradient-type algorithms.
Journal of Optimization Theory and Applications, 98 (3), September 1998.
O.L. Mangasarian and M.V. Solodov: Backpropagation Convergence Via Deterministic Perturbed Minimization.
Advances in Neural Information Processing Systems 6,
J.D. Cowan, G. Tesauro and J. Alspector (eds), Morgan Kaufmann Publishers, San Francisco, CA, 1994, 383-390.

You can access my other research papers in Mathematical Programming from my home page.

Back to the Machine Learning in Mathematical Programming page.