A smoothing-regularization method for mathematical programs with cardinality constraints
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Bibliographic record
Abstract
A cardinality constraint in an optimization problem limits the number of nonzeroentries in each element of the solution set. Traditional methods, such as branch-andbound,can reduce the number of feasible points to search. That said, many ofthe proposed methods to solve mathematical programs with cardinality constraintsstill have a computational complexity which is exponential. Previous work has reformulatedcardinality constrained mathematical programs (with dierentiable constraintsand objectives) as mathematical programs with complementarity constraints(MPCCs) which preserve the global and local minimizers of the original problem.Similar to previous work with MPCCs, this gave way to regularization approacheswhich allow standard NLP solvers to be eectively used. In Chapters 3, we investigatethe theoretical properties of a new regularization approach by considering itsconvergence properties. Additionally, Chapter 4 uses the regularization approachto solve a cardinality constrained non-convex objective function. In doing this, wefurther improve on the numerical understandings of the Scholtes-type regularizationapproach while demonstrating that regularization can be eectively employed evenwith a non-convex objective
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.005 |
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