报告题目：Treating Cardinality Constraint within the Framework of Interval Branch and Bound for Solving the Best Subset Selection Problem

主  讲 人：Min Sun 教授

单      位：阿拉巴马大学（美国）

时      间：2024年6月14日 16:00

地      点：学院一楼报告厅

摘     要：Many real-world problems in natural science, engineering, statistics, social sciences, and economics can be modeled as continuous global optimization problems. Sometimes, problems would also require us to choose only a handful of parameters from a large number of available parameters, resulting in a cardinality-constrained optimization problem. Cardinality-constraint is often conveniently treated indirectly through special penalty functions. Well-known examples of such indirect approach include ridge regression (l2-penalty), LASSO (l1-penalty), and elastic net (l1-l2 mixed penalty). Cardinality-constraint can also be treated directly to ensure that only a desired small number of parameters are selected in the final optimal solution. Penalty based indirect approach allows almost all existing optimization techniques to be applicable immediately. However, conventional interval branch and bound (IBB) methods do not accept the cardinality-constraint. In this talk, we use the best subset selection (BSS) problem as an example to discuss how the framework of IBB could be modified to accommodate the cardinality-constraint. BSS is a classical problem in statistics that requires choosing a subset from a larger number of available variables to be included in the model which minimizes the residual sum of squares in the linear regression. IBB is a well-known method to solve global optimization problems even when the feasible set is non-convex. We modified main features of the IBB to treat the cardinality-constraint effectively. The resulting algorithm gives a procedure to enumerate all the candidate solutions and discard the sub-optimal solutions by using deletion conditions to finally locate an optimal solution. We also talk about some related optimal and suboptimal algorithms. Finally we report some results of numerical experiments to validate the effectiveness of our methods for solving BSS problem.

简      介：Dr. Min Sun is a Full Professor of Department of Mathematics in the University of Alabama. Dr. Sun obtained his Ph.D. in Applied Mathematics from Wayne State University in 1987. Dr. Sun’s research areas are global optimization, optimal control, minimax and game, multi-objective programming, modeling and simulation with applications in smart and autonomous home energy managements, water resources management, magnetic materials research, and traffic managements. Research results have been published in a variety of international scientific journals in several different areas.