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On Integer and MPCC Representability of Affine Sparsity

Hongbo Dong (hongbo.dong***at***wsu.edu)

Abstract: In addition to sparsity, practitioners of statistics and machine learning often wish to promote additional structures in their variable selection process to incorporate prior knowledge. Borrowing the modeling power of linear systems with binary variables, many of such structures can be faithfully modeled as so-called affine sparsity constraints (ASC). In this note we study conditions under which an ASC system can be represented by sets in integer programs and mathematical programs with complementarity conditions (MPCC). Results of this note facilitate developing nonconvex optimization methods for variable selection with structured sparsity.

Keywords: Structured sparsity, Integer program, Mathematical program with complementarity conditions

Category 1: Complementarity and Variational Inequalities

Category 2: Integer Programming ((Mixed) Integer Nonlinear Programming )

Citation: Working paper, Department of Mathematics and Statistics, Washington State University

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Entry Submitted: 04/16/2018
Entry Accepted: 04/16/2018
Entry Last Modified: 04/17/2018

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