Related papers: Convexifying Multilinear Sets with Cardinality Con…
Simple cardinality refers to counting nonzero elements of an independent variable satisfying certain properties. Composite cardinality is a simple counting process composited with an affine mapping, and is therefore more complicated than…
Boolean Satisfiability Problem (SAT) is one of the core problems in computer science. As one of the fundamental NP-complete problems, it can be used - by known reductions - to represent instances of variety of hard decision problems.…
In the present paper, classical tools of convex analysis are used to study the solution set to a certain class of set-inclusive generalized equations. A condition for the solution existence and global error bounds is established, in the…
Let $H$ be a real Hilbert space. In this short note, using some of the properties of bounded linear operators with closed range defined on $H$, certain bounds for a specific convex subset of the solution set of infinite linear…
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…
We consider convex constrained optimization problems that also include a cardinality constraint. In general, optimization problems with cardinality constraints are difficult mathematical programs which are usually solved by global…
In this paper, we study the solution uniqueness of an individual feasible vector of a class of convex optimization problems involving convex piecewise affine functions and subject to general polyhedral constraints. This class of problems…
We investigate new convex relaxations for the pooling problem, a classic nonconvex production planning problem in which input materials are mixed in intermediate pools, with the outputs of these pools further mixed to make output products…
In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix…
A planar point set is in convex position precisely when it has a convex polygonization, that is, a polygonization with maximum interior angle measure at most \pi. We can thus talk about the convexity of a set of points in terms of the…
In this paper, we investigate the polyhedral structure of two submodular sets with generalized upper bound (GUB) constraints, which arise as important substructures in various real-world applications. We derive a class of strong valid…
We consider binary classification restricted to a class of continuous piecewise linear functions whose decision boundaries are (possibly nonconvex) starshaped polyhedral sets, supported on a fixed polyhedral simplicial fan. We investigate…
This paper deals with the regularization of the sum of functions defined on a locally convex spaces through their closed-convex hulls in the bidual space. Different conditions guaranteeing that the closed-convex hull of the sum is the sum…
Consider reconstructing a signal $x$ by minimizing a weighted sum of a convex differentiable negative log-likelihood (NLL) (data-fidelity) term and a convex regularization term that imposes a convex-set constraint on $x$ and enforces its…
L$^\natural$ (natural)-convex functions encompass a large class of nonlinear functions over general integer domains and arise in a wide range of real-world applications. We explore the minimization of L$^\natural$-convex functions, of…
This paper studies the problem of reconstructing binary matrices that are only accessible through few evaluations of their discrete X-rays. Such question is prominently motivated by the demand in material science for developing a tool for…
Discretization-based methods have been proposed for solving nonconvex optimization problems with bilinear terms such as the pooling problem. These methods convert the original nonconvex optimization problems into mixed-integer linear…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
A multiobjective optimization problem is $C^r$ simplicial if the Pareto set and the Pareto front are $C^r$ diffeomorphic to a simplex and, under the $C^r$ diffeomorphisms, each face of the simplex corresponds to the Pareto set and the…
The Planar Contraction problem is to test whether a given graph can be made planar by using at most k edge contractions. This problem is known to be NP-complete. We show that it is fixed-parameter tractable when parameterized by k.