相关论文: Facets of a mixed-integer bilinear covering set wi…

We consider a general conic mixed-binary set where each homogeneous conic constraint $j$ involves an affine function of independent continuous variables and an epigraph variable associated with a nonnegative function, $f_j$, of common…

Seeking the convex hull of an object is a very fundamental problem arising from various tasks. In this work, we propose two variational convex hull models using level set representation for 2-dimensional data. The first one is an exact…

We study the convex hull of a set $S\subset \mathbb{R}^n$ defined by three quadratic inequalities. A simple way of generating inequalities valid on $S$ is to take nonnegative linear combinations of the defining inequalities of $S$. We call…

We consider bounded integer knapsacks where the weights and variable upper bounds together form a superincreasing sequence. The elements of this superincreasing knapsack are exactly those vectors that are lexicographically smaller than the…

We consider the bipartite boolean quadric polytope (BQP) with multiple-choice constraints and analyse its combinatorial properties. The well-studied BQP is defined as the convex hull of all quadric incidence vectors over a bipartite graph.…

Balas introduced disjunctive cuts in the 1970s for mixed-integer linear programs. Several recent papers have attempted to extend this work to mixed-integer conic programs. In this paper we study the structure of the convex hull of a…

We consider an $n$-variate monomial function that is restricted both in value by lower and upper bounds and in domain by two homogeneous linear inequalities. Such functions are building blocks of several problems found in practical…

This paper introduces mixed-integer optimization methods to solve regression problems that incorporate fairness metrics. We propose an exact formulation for training fair regression models. To tackle this computationally hard problem, we…

A new approach to the local and global explanation is proposed. It is based on selecting a convex hull constructed for the finite number of points around an explained instance. The convex hull allows us to consider a dual representation of…

Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…

We study the polyhedral structure of the static probabilistic lot-sizing problem and propose valid inequalities that integrate information from the chance constraint and the binary setup variables. We prove that the proposed inequalities…

The infinite models in integer programming can be described as the convex hull of some points or as the intersection of halfspaces derived from valid functions. In this paper we study the relationships between these two descriptions. Our…

We propose a method to generate cutting-planes from multiple covers of knapsack constraints. The covers may come from different knapsack inequalities if the weights in the inequalities form a totally-ordered set. Thus, we introduce and…

Arithmetic automata recognize infinite words of digits denoting decompositions of real and integer vectors. These automata are known expressive and efficient enough to represent the whole set of solutions of complex linear constraints…

We study properties of convex hulls of (co)adjoint orbits of compact groups, with applications to invariant theory and tensor product decompositions. The notion of partial convex hulls is introduced and applied to define two numerical…

We consider the multilinear polytope defined as the convex hull of the set of binary points satisfying a collection of multilinear equations. The complexity of the facial structure of the multilinear polytope is closely related to the…

In this paper, we consider the polyhedral structure of the unit commitment polytope. In particular, we provide the convex hull results for the problem under the following different settings: 1) the convex hulls for the integrated…

The convex hull of N independent random points chosen on the boundary of a simple polytope in R^n is investigated. Asymptotic formulas for the expected number of vertices and facets, and for the expectation of the volume difference are…

A classical approach for obtaining valid inequalities for a set involves weighted aggregations of the inequalities that describe such set. When the set is described by linear inequalities, thanks to the Farkas lemma, we know that every…

Let V be a semialgebraic set parameterized by quadratic polynomials over a quadratic set T. This paper studies semidefinite representation of its convex hull by projections of spectrahedra (defined by linear matrix inequalities). When T is…