Related papers: Diameter Polytopes of Feasible Binary Programs
This paper describes an approximate method for global optimization of polynomial programming problems with bounded variables. The method uses a reformulation and linearization technique to transform the original polynomial optimization…
We study optimal decision policies for integer linear programs with a fixed feasible set and varying cost vectors, represented as linear decision trees. Once synthesized for a given feasible set, they return an optimal solution for any…
We consider the line planning problem in public transport in the Parametric City, an idealized model that captures typical scenarios by a (small) number of parameters. The Parametric City is rotation symmetric, but optimal line plans are…
We establish a complete classification of binary group codes with complementary duals for a finite group and explicitly determine the number of linear complementary dual (LCD) cyclic group codes by using cyclotomic cosets. The dimension and…
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…
The present paper is devoted to studying of minimal parametric fillings of finite metric spaces (a version of optimal connection problem) by methods of Linear Programming. The estimate on the multiplicity of multi-tours appearing in the…
Binary optimal codes often contain optimal or near-optimal subcodes. In this paper we show that this is true for the family of self-dual codes. One approach is to compute the optimum distance profiles (ODPs) of linear codes, which was…
This thesis describes a numerical study of binary boson stars within the context of an approximation to general relativity. The approximation we adopt places certain restrictions on the dynamical variables of general relativity (conformal…
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…
The prime focus of this paper is the study of optimal duals of a given finite frame as well as optimal dual pairs, in the context of probability modelled erasures of frame coefficients. We characterize optimal dual frames (and dual pairs)…
Recent interest on permutation rank modulation shows the Kendall tau metric as an important distance metric. This note documents our first efforts to obtain upper bounds on optimal code sizes (for said metric) ala Delsarte's approach. For…
In real-world applications, users often favor structurally diverse design choices over one high-quality solution. It is hence important to consider more solutions that decision makers can compare and further explore based on additional…
We study a submodular maximization problem motivated by applications in online retail. A platform displays a list of products to a user in response to a search query. The user inspects the first $k$ items in the list for a $k$ chosen at…
We study a class of procurement auctions with a budget constraint, where an auctioneer is interested in buying resources or services from a set of agents. Ideally, the auctioneer would like to select a subset of the resources so as to…
We study time-varying semidefinite programs (TV-SDPs), which are semidefinite programs whose data (and solutions) are functions of time. Our focus is on the setting where the data varies polynomially with time. We show that under a strict…
When modeling an application of practical relevance as an instance of a combinatorial problem X, we are often interested not merely in finding one optimal solution for that instance, but in finding a sufficiently diverse collection of good…
One cannot make truly fair decisions using integer linear programs unless one controls the selection probabilities of the (possibly many) optimal solutions. For this purpose, we propose a unified framework when binary decision variables…
Diversity maximization is an important geometric optimization problem with many applications in recommender systems, machine learning or search engines among others. A typical diversification problem is as follows: Given a finite metric…
We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and…
We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane arrangements. Using our decomposition, we bound the number of…