Related papers: Decision Problems in Multilevel Linear Programming
Delsarte's method and its extensions allow to consider the upper bound problem for codes in 2-point-homogeneous spaces as a linear programming problem with perhaps infinitely many variables, which are the distance distribution. We show that…
In [SIAM J. Optim., 2022], the authors introduced a new linear programming (LP) relaxation for K-means clustering. In this paper, we further investigate both theoretical and computational properties of this relaxation. As evident from our…
We study a class of countably-infinite-dimensional linear programs (CILPs) whose feasible sets are bounded subsets of appropriately defined spaces of measures. The optimal value, optimal points, and minimal points of these CILPs can be…
Let ${\cal L}$ be an arrangement of $n$ lines in the Euclidean plane. The \emph{$k$-level} of ${\cal L}$ consists of all vertices $v$ of the arrangement which have exactly $k$ lines of ${\cal L}$ passing below $v$. The complexity (the…
One of the main problems in random network coding is to compute good lower and upper bounds on the achievable cardinality of the so-called subspace codes in the projective space $\mathcal{P}_q(n)$ for a given minimum distance. The…
This paper considers the computational hardness of computing expected outcomes and deciding almost-sure termination of probabilistic programs. We show that deciding almost-sure termination and deciding whether the expected outcome of a…
We consider the ILP Feasibility problem: given an integer linear program $\{Ax = b, x\geq 0\}$, where $A$ is an integer matrix with $k$ rows and $\ell$ columns and $b$ is a vector of $k$ integers, we ask whether there exists…
This paper studies, for the first time, a bilevel polynomial program whose constraints involve uncertain linear constraints and another uncertain linear optimization problem. In the case of box data uncertainty, we present a sum of squares…
Linear programming on the Stiefel manifold (LPS) is studied for the first time. It aims at minimizing a linear objective function over the set of all $p$-tuples of orthonormal vectors in ${\mathbb R}^n$ satisfying $k$ additional linear…
We propose an exact method which combines the resolution search and branch & bound algorithms for solving the 0?1 Multidimensional Knapsack Problem. This algorithm is able to prove large?scale strong correlated instances. The optimal values…
It is a well-known result that bilevel linear optimization is NP-hard. In many publications, reformulations as mixed-integer linear optimization problems are proposed, which suggests that the decision version of the problem belongs to NP.…
In this paper, we consider the infinite-dimensional integration problem on weighted reproducing kernel Hilbert spaces with norms induced by an underlying function space decomposition of ANOVA-type. The weights model the relative importance…
It is well-known that coupling constraints in linear bilevel optimization can lead to disconnected feasible sets, which is not possible without coupling constraints. However, there is no difference between linear bilevel problems with and…
This paper introduces a concept of a derivative of the optimal value function in linear programming (LP). Basically, it is the the worst case optimal value of an interval LP problem when the nominal data the data are inflated to intervals…
We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…
We study optimization programs given by a bilinear form over non-commutative variables subject to linear inequalities. Problems of this form include the entangled value of two-prover games, entanglement-assisted coding for classical…
Absolute value linear programming problems is quite a new area of optimization problems, involving linear functions and absolute values in the description of the model. In this paper, we consider interval uncertainty of the input…
In this paper we examine multi-objective linear programming problems in the face of data uncertainty both in the objective function and the constraints. First, we derive a formula for radius of robust feasibility guaranteeing constraint…
We study two-stage robust optimization problems with mixed discrete-continuous decisions in both stages. Despite their broad range of applications, these problems pose two fundamental challenges: (i) they constitute infinite-dimensional…
The accuracy and complexity of machine learning algorithms based on kernel optimization are limited by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…