In this work, we study continuous reformulations of zero-one concave programming problems. We introduce new concave penalty functions and we prove, using general equivalence results here derived, that the obtained continuous problems are equivalent to the original combinatorial problem.

We consider the problem of minimizing a class of quasi-concave functions over a convex set. Quasiconcave functions are a generalization of concave functions and thus, NP-hard to minimize over a convex set in general. We present a simple fully polynomial time approximation scheme (FPTAS) for minimizing a fairly general class of low-rank quasi-concave functions. Our algorithm is based on solving ...

Measures for sparse best–basis selection are analyzed and shown to fit into a general framework based on majorization, Schur-concavity, and concavity. This framework facilitates the analysis of algorithm performance and clarifies the relationships between existing proposed concentration measures useful for sparse basis selection. It also allows one to define new concentration measures, and seve...

Discrete strip-concave functions considered in this paper are, in fact, equivalent to an extension of Gelfand-Tsetlin patterns to the case when the pattern has a not necessarily triangular but convex configuration. They arise by releasing one of the three types of rhombus inequalities for discrete concave functions (or “hives”) on a “convex part” of a triangular grid. The paper is devoted to a ...

The concepts of L-convex function and M-convex function have recently been introduced by Murota as generalizations of submodular function and base polyhedron, respectively, and discrete separation theorems are established for L-convex/concave functions and for M-convex/concave functions as generalizations of Frank's discrete separation theorem for submodular/supermodular set functions and Edmon...

In this paper, we introduce a more general approach to the fuzzification of fuzzy concavity. More specifically, degree L , M -fuzzy concavity is introduced and characterized as generalization id="M2"> -concave structure id="M3"> conca...