Cardinality constrained combinatorial optimization: Complexity and polyhedra

Cardinality constrained combinatorial optimization: Complexity and polyhedra

Given a combinatorial optimization problem and a subset N of natural numbers, we obtain a cardinality constrained version of this problem by permitting only those feasible solutions whose cardinalities are elements of N . In this paper we briefly touch on questions that addresses common grounds and differences of the complexity of a combinatorial optimization problem and its cardinality constra...

Parameterized Complexity of Cardinality Constrained Optimization Problems

We study the parameterized complexity of cardinality constrained optimization problems, i.e. optimization problems that require their solutions to contain specified numbers of elements to optimize solution values. For this purpose, we consider around 20 such optimization problems, as well as their parametric duals, that deal with various fundamental relations among vertices and edges in graphs....

Integer Polyhedra: Combinatorial Properties and Complexity

Algorithm for cardinality-constrained quadratic optimization

This paper describes an algorithm for cardinality-constrained quadratic optimization problems, which are convex quadratic programming problems with a limit on the number of non-zeros in the optimal solution. In particular, we consider problems of subset selection in regression and portfolio selection in asset management and propose branch-and-bound based algorithms that take advantage of the sp...

A short note on the robust combinatorial optimization problems with cardinality constrained uncertainty

Robust combinatorial optimization problems with cardinality constrained uncertainty may be solved by a finite number of nominal problems. In this paper, we show that the number of nominal problems to be solved can be reduced significantly.