Sparsity constrained optimization problems via disjunctive programming. (3rd October 2022)

• Record Type: Journal Article
• Authors: Movahedian, N.; Nobakhtian, S.; Sarabadan, M.
• Is Part Of: Optimization. Volume 71:Number 10(2022)
• Page Start: 2979
• Page End: 3005
• Publication Date: 2022-10-03
• Subjects: Nonlinear programming -- sparsity constrained optimization -- stationarity -- optimality conditions -- constraint qualification; 90C26 -- 90C46 -- 90C90; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1892675
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we consider the problem of minimizing a continuously differentiable function subject to sparsity constraints. We formulate this problem as an equivalent disjunctive constrained optimization program. Then, we extend some of the well-known constraint qualifications by using the contingent and normal cones of the sparsity set and show that these constraint qualifications can be applied to obtain the first-order optimality conditions. In addition, we give the first-order sufficient optimality conditions by defining a new generalized convexity notion. Furthermore, we present the second-order necessary and sufficient optimality conditions for sparsity constrained optimization problems. Finally, we provide some examples and special cases to illustrate the obtained results.