Related papers: On Subadditive Duality for Conic Mixed-Integer Pro…

We design new tools to study variants of Total Dual Integrality. As an application, we obtain a geometric characterization of Total Dual Integrality for the case where the associated polyhedron is non-degenerate. We also give sufficient…

There is often a significant trade-off between formulation strength and size in mixed integer programming (MIP). When modeling convex disjunctive constraints (e.g. unions of convex sets), adding auxiliary continuous variables can sometimes…

In this paper we provide characterizing properties of TDI systems, among others the following: a system of linear inequalities is TDI if and only if its coefficient vectors form a Hilbert basis, and there exists a test-set for the system's…

A fundamental theorem in discrete convex analysis states that a set function is M$^\natural$-concave if and only if its conjugate function is submodular. This paper gives a new proof to this fact.

Consider a convex set S defined by a matrix inequality of polynomials or rational functions over a domain. The set S is called semidefinite programming (SDP) representable or just semidefinite representable if it equals the projection of a…

An integer program is called ideal if its continuous relaxation coincides with its convex hull allowing the problem to be solved as a continuous program and offering substantial computational advantages. Proving idealness analytically can…

Led by a result derived from Sion's minimax theorem concerning constraint violation in quadratically constrained quadratic programs (QCQPs) with at least one constraint bounding the possible solution magnitude, we propose a heuristic scheme…

A classic result of Lenstra [Math.~Oper.~Res.~1983] says that an integer linear program can be solved in fixed-parameter tractable (FPT) time for the parameter being the number of variables. We extend this result by incorporating…

We optimize the running time of the primal-dual algorithms by optimizing their stopping criteria for solving convex optimization problems under affine equality constraints, which means terminating the algorithm earlier with fewer…

We review the notion of symplectic duality earlier introduced in the context of topological recursion. We show that the transformation of symplectic duality can be expressed as a composition of $x-y$ dualities in a broader context of log…

We give a simple example of a set that is weakly Dedekind infinite (= can be mapped onto omega) but dually Dedekind finite (=cannot be mapped noninjectively onto itself), namely, the power set of a superamorphous set. (A infinite set is…

We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariate quadratic functions due to Yarotsky, formulating this…

In this paper we introduce a new dual program, which is representable as a semi-definite linear programming problem, for a primal convex minimax programming model problem and show that there is no duality gap between the primal and the dual…

Given an effective Q-divisor D on a smooth complex variety, one can associate to D its multiplier ideal sheaf J(D), which measures in a somewhat subtle way the singularities of D. Because of their strong vanishing properties, these ideals…

Mixability is a property of a loss which characterizes when fast convergence is possible in the game of prediction with expert advice. We show that a key property of mixability generalizes, and the exp and log operations present in the…

In this paper, we consider the canonical water network design problem, which contains nonconvex potential loss functions and discrete resistance choices with varying costs. Traditionally, to resolve the nonconvexities of this problem,…

This article is devoted to investigate a nonsmooth/nonconvex uncertain multiobjective optimization problem with composition fields (CUP) for brevity) over arbitrary Asplund spaces. Employing some advanced techniques of variational analysis…

In this work, we add an additional condition to strong pseudo prime test to base 2. Then, we provide theoretical and heuristics evidences showing that the resulting algorithm catches all composite numbers. Our method is based on the…

This paper discusses the split feasibility problem with polynomials. The sets are semi-algebraic, defined by polynomial inequalities. They can be either convex or nonconvex, either feasible or infeasible. We give semidefinite relaxations…

We connect high-dimensional subset selection and submodular maximization. Our results extend the work of Das and Kempe (2011) from the setting of linear regression to arbitrary objective functions. For greedy feature selection, this…