Abstract Recently, a new approach to tackle cardinality-constrained optimization problems based on continuous reformulation of the problem was proposed. Following this approach, we derive problem-tailored sequential optimality condition, which is satisfied at every local minimizer without requiring any constraint qualification. We relate condition an existing M-type stationary concept by introd...

We study the polyhedral convex hull structure of a mixed-integer set which arises in class cardinality-constrained concave submodular minimization problems. This problems has an objective function form $$f(a^\top x)$$ , where f is univariate function, non-negative vector, and x binary vector appropriate dimension. Such frequently appear applications that involve risk-aversion or economies scale...