Hear Dr. Ouayl Chadli in the mathematics department explain minimax techniques in optimal control problems and machine learning.
Abstract:
In this talk, we present some recent results from our contributions to the study of the existence and optimal control of Nonlinear Evolution Problems, as well as accelerated methods in Machine Learning Problems by a minimax inequality approach. Our study is motivated by the fact that many control problems arising in physical and engineering problems, whose state system is a variational inequality problem or a nonlinear evolution equation, or a hemivariational inequality problem, can be modeled as a control problem governed by a mixed minimax inequality. There are different techniques for studying the existence of solutions for optimal control problems governed by nonlinear evolution equations, variational inequalities, or hemivariational inequalities in the literature. However, the technique which I will describe in this presentation is completely different from the ex- isting ones. It is based on a constructive Galerkin-type method using a minimax inequality associated with a maximal monotone bifunction and a pseudomonotone bifunction in the sense of Bre ́zis, and a stability result associated with the Mosco convergence.
In the second part, we discuss minimax technics in solving Stochastic Variational Inequalities (SVI). SVIs have recently found many applications in data analysis, especially in machine learning models helping to represent massive data compactly. We present a novel method for solving a mono- tone class of Stochastic Variational Inequalities (SVI). In our approach, we propose an accelerated algorithm combining the mirror-proximal method and a descent method for minimax inequalities through a compatible regularized gap function corresponding to the standard optimality criteria in the aforementioned problem. Our algorithm does not require a priori knowledge about smoothness or non smoothness of the objective function and the noise properties of the problem. Optimal error bounds are obtained and an application to an overlapped group lasso problem is provided.
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The UCF Mathematics and Applications Seminar, which takes place every Friday from 11 a.m. to 12 p.m. in MSB 318, provides a venue for researchers to present their current work, foster new collaborations, and showcase both foundational mathematics and its applications to graduate and undergraduate students.
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