Sparsity constrained optimization problems via disjunctive programming

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 continge...

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Published inOptimization Vol. 71; no. 10; pp. 2979 - 3005
Main Authors Movahedian, N., Nobakhtian, S., Sarabadan, M.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 03.10.2022
Taylor & Francis LLC
Subjects
constraint qualification
Constraints
Convexity
Nonlinear programming
optimality conditions
Optimization
sparsity constrained optimization
stationarity
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Summary: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.
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content type line 14
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2021.1892675