Related papers: Optimal cutting planes from the group relaxations
We study an abstract setting for cutting planes for integer programming called the infinite group problem. In this abstraction, cutting planes are computed via cut generating function that act on the simplex tableau. In this function space,…
In this note we announce the availability of an electronic compendium of extreme functions for Gomory--Johnson's infinite group problem. These functions serve as the strongest cut-generating functions for integer linear optimization…
In this self-contained paper, we present a theory of the piecewise linear minimal valid functions for the 1-row Gomory-Johnson infinite group problem. The non-extreme minimal valid functions are those that admit effective perturbations. We…
Let G be a compact group acting in a real vector space V. We obtain a number of inequalities relating the L^infinity norm of a matrix element of the representation of G with its L^p norm for p<infinity. We apply our results to obtain…
Maximin fairness is the ideal that the worst-off group (or individual) should be treated as well as possible. Literature on maximin fairness in various decision-making settings has grown in recent years, but theoretical results are sparse.…
We give an algorithm for testing the extremality of minimal valid functions for Gomory and Johnson's infinite group problem that are piecewise linear (possibly discontinuous) with rational breakpoints. This is the first set of necessary and…
We present a version of GMI (Gomory mixed-integer) cuts in a way so that they are derived with respect to a "dual form" mixed-integer optimization problem and applied on the standard-form primal side as columns, using the primal simplex…
We consider the problem of estimating a good maximizer of a black-box function given noisy examples. To solve such problems, we propose to fit a new type of function which we call a global optimization network (GON), defined as any…
In this paper, we are interested in the analysis of a well-known free boundary/shape optimization problem motivated by some issues arising in population dynamics. The question is to determine optimal spatial arrangements of favorable and…
We give a variant of Basu-Hildebrand-Molinaro's approximation theorem for continuous minimal valid functions for Gomory-Johnson's infinite group problem by piecewise linear two-slope extreme functions [Minimal cut-generating functions are…
Consider a convex function that is invariant under an group of transformations. If it has a minimizer, does it also have an invariant minimizer? Variants of this problem appear in nonparametric statistics and in a number of adjacent fields.…
The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-$s$ principal submatrix of an order-$n$ covariance…
This note further addresses the global optimization problem for max-plus linear systems considered in [Automatica 119 (2020) 109104]. Firstly, the operations between infinity elemens and real numbers involved in the formulas of solving…
We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though…
Many operations related optimization problems involve repeatedly solving similar mixed integer linear programming (MILP) instances with the same constraint matrix but differing objective coefficients and right-hand-side values. The goal of…
We investigate existence, uniqueness and maximality of solutions $T$ for equations $S_1+T=S_2$ and inequalities $S_1+T\subseteq S_2$ where $S_1$ and $S_2$ are final segments of ordered abelian groups. Since cuts are determined by their…
This paper settles the existence question for a rather general class of convex optimal design problems with a volume constraint. In low dimensions, we prove the existence of an optimal configuration for general convex minimization problems…
We provide a generalization of first-order necessary conditions of optimality for infinite-dimensional optimization problems with a finite number of inequality constraints and with a finite number of inequality and equality constraints. Our…
The generalized Fitting height of a finite group $G$ is the least number $h=h^*(G)$ such that $F^*_h(G)=G$, where the $F^*_i(G)$ is the generalized Fitting series: $F^*_1(G)=F^*(G)$ and $F^*_{i+1}(G)$ is the inverse image of…
In this paper, we study the classic submodular maximization problem subject to a group equality constraint under both non-adaptive and adaptive settings. It has been shown that the utility function of many machine learning applications,…