Related papers: Unique lifting of integer variables in minimal ine…
We consider mixed integer linear sets defined by two equations involving two integer variables and any number of non-negative continuous variables. The non-trivial valid inequalities of such sets can be classified into split, type 1, type…
This work is concerned with the convex analysis of functions defined on (not necessarily finite-dimensional) Hilbert spaces whose values depend solely on a certain ``spectrum'' of the arguments, a class we term ``spectral functions.'' We…
Lifting theorems are theorems that bound the communication complexity of a composed function $f\circ g^{n}$ in terms of the query complexity of $f$ and the communication complexity of $g$. Such theorems constitute a powerful generalization…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
Bilevel programs model sequential decision interactions between two sets of players and find wide applications in real-world complex systems. In this paper, we consider a bilevel mixed-integer linear program with binary tender, wherein the…
Many results in mass partitions are proved by lifting $\mathbb{R}^d$ to a higher-dimensional space and dividing the higher-dimensional space into pieces. We extend such methods to use lifting arguments to polyhedral surfaces. Among other…
Sequence-independent lifting is a procedure for strengthening valid inequalities of an integer program. We generalize the sequence-independent lifting method of Gu, Nemhauser, and Savelsbergh (GNS lifting) for cover inequalities and correct…
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 note, we derive a uniqueness theorem for minimal graphs of general codimension under certain restrictions closed related to the convexity (not strict convexity) of the area functional with respect to singular values, improving the…
We present a technique for automatically extracting mutual exclusion invariants from temporal planning instances. It first identifies a set of invariant templates by inspecting the lifted representation of the domain and then checks these…
Piecewise affine functions are widely used to approximate nonlinear and discontinuous functions. However, most, if not all existing models only deal with fitting continuous functions. In this paper, we investigate the problem of fitting a…
The purpose of this paper is to analyze a nonlinear elasticity model introduced by the authors for comparing two images, regarded as bounded open subsets of $\R^n$ together with associated vector-valued intensity maps. Optimal…
Recently, there was a substantial progress in the problem of sampling recovery on function classes with mixed smoothness. Mostly, it has been done by proving new and sometimes optimal upper bounds for both linear sampling recovery and for…
In this paper, analytic relations between the macroscopic variables and the mesoscopic variables are derived for lattice Boltzmann methods (LBM). The analytic relations are achieved by two different methods for the exchange from velocity…
Mixed-integer convex quadratic programs with indicator variables (MIQP) encompass a wide range of applications, from statistical learning to energy, finance, and logistics. The outer approximation (OA) algorithm has been proven efficient in…
Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb…
In discrete convex analysis, the scaling and proximity properties for the class of L$^\natural$-convex functions were established more than a decade ago and have been used to design efficient minimization algorithms. For the larger class of…
In this paper, we consider a class of mixed integer programming problems (MIPs) whose objective functions are DC functions, that is, functions representable in terms of the difference of two convex functions. These MIPs contain a very wide…
Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis. We introduce a new class of upper bounds on the log partition…
Decoupling inequalities disentangle complex dependence structures of random objects so that they can be analyzed by means of standard tools from the theory of independent random variables. We study decoupling inequalities for vector-valued…