相关论文: Polyhedral results for two classes of submodular s…

Distributionally robust optimization is used to tackle decision making problems under uncertainty where the distribution of the uncertain data is ambiguous. Many ambiguity sets have been proposed for continuous uncertainty that build on…

Let $G$ be a simple simply connected algebraic group over an algebraically closed field $k$ of characteristic $p$, with Frobenius kernel $G_{(1)}$. It is known that when $p\ge 2h-2$, where $h$ is the Coxeter number of $G$, the projective…

We prove that the combinatorial optimization problem of determining the hull number of a partial cube is NP-complete. This makes partial cubes the minimal graph class for which NP-completeness of this problem is known and improves some…

Cutting planes are frequently used for solving integer programs. A common strategy is to derive cutting planes from building blocks or a substructure of the integer program. In this paper, we focus on knapsack constraints that arise from…

A programming tactic involving polyhedra is reported that has been widely applied in the polyhedral analysis of (constraint) logic programs. The method enables the computations of convex hulls that are required for polyhedral analysis to be…

The well-known sequentially lifted cover inequality is widely employed in solving mixed integer programs. However, it is still an open question whether a sequentially lifted cover inequality can be computed in polynomial time for a given…

Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the…

In this proceedings, I outline recent efforts to constrain models based on generalized uncertainty principles (GUP) using limits on coefficients of the Standard-Model Extension. Two main results are reported: (1) bounds on isotropic GUP…

This paper addresses the study and applications of polyhedral duality of locally convex topological vector (LCTV) spaces. We first revisit the classical Rockafellar's proper separation theorem for two convex sets one which is polyhedral and…

Optimization of DR-submodular functions has experienced a notable surge in significance in recent times, marking a pivotal development within the domain of non-convex optimization. Motivated by real-world scenarios, some recent works have…

We investigate a mixed 0-1 conic quadratic optimization problem with indicator variables arising in mean-risk optimization. The indicator variables are often used to model non-convexities such as fixed charges or cardinality constraints.…

Rough sets are efficient for data pre-processing in data mining. As a generalization of the linear independence in vector spaces, matroids provide well-established platforms for greedy algorithms. In this paper, we apply rough sets to…

In the present work, we consider Zuckerberg's method for geometric convex-hull proofs introduced in [Geometric proofs for convex hull defining formulations, Operations Research Letters 44(5), 625-629 (2016)]. It has only been scarcely…

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.…

We investigate the motions of a bar structure consisting of two congruent tetrahedra, whose edges in their basic position form the face diagonals of a rectangular parallelepiped. The constraint of the motion is that the originally…

Robust optimization is becoming increasingly important in machine learning applications. In this paper, we study a unified framework of robust submodular optimization. We study this problem both from a minimization and maximization…

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…

The convex hull generated by the restriction to the unit ball of a stationary Poisson point process in the $d$-dimensional Euclidean space is considered. By establishing sharp bounds on cumulants, exponential estimates for large deviation…

Geometric hitting set problems, in which we seek a smallest set of points that collectively hit a given set of ranges, are ubiquitous in computational geometry. Most often, the set is discrete and is given explicitly. We propose new…

Error bounds are central objects in optimization theory and its applications. They were for a long time restricted only to the theory before becoming over the course of time a field of itself. This paper is devoted to the study of error…