Related papers: Linear Programming Complementation
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
Multilevel programming is the standard framework for modeling hierarchical decision-making. In this paper, we characterize the computational complexity of deciding the existence of feasible and optimal solutions, as well as computing the…
Quadratic Programming (QP) is the well-studied problem of maximizing over {-1,1} values the quadratic form \sum_{i \ne j} a_{ij} x_i x_j. QP captures many known combinatorial optimization problems, and assuming the unique games conjecture,…
The sum-rank metric provides a unifying framework that generalizes both the celebrated Hamming and rank metrics, and has found applications in areas such as network coding, distributed storage, and space-time coding. A central problem is to…
We study a family of combinatorial optimization problems defined by a parameter $p\in[0,1]$, which involves spectral functions applied to positive semidefinite matrices, and has some application in the theory of optimal experimental design.…
We propose a linear programming (LP) framework for steady-state diffusion and flux optimization on geometric networks. The state variable satisfies a discrete diffusion law on a weighted, oriented graph, where conductances are scaled by…
Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…
We consider the general polynomial optimization problem $P: f^*=\min \{f(x)\,:\,x\in K\}$ where $K$ is a compact basic semi-algebraic set. We first show that the standard Lagrangian relaxation yields a lower bound as close as desired to the…
In this work, we reveal a rich combinatorial structure underlying exact minimax optimal algorithms for classical nonexpansive fixed-point problems. This viewpoint unifies all extremal optimal methods and provides a systematic and practical…
A popular method in combinatorial optimization is to express polytopes P, which may potentially have exponentially many facets, as solutions of linear programs that use few extra variables to reduce the number of constraints down to a…
Let $A$ and $B$ be two point sets in the plane of sizes $r$ and $n$ respectively (assume $r \leq n$), and let $k$ be a parameter. A matching between $A$ and $B$ is a family of pairs in $A \times B$ so that any point of $A \cup B$ appears in…
We study a generalization of the Set Cover problem called the \emph{Partial Set Cover} in the context of geometric set systems. The input to this problem is a set system $(X, \mathcal{S})$, where $X$ is a set of elements and $\mathcal{S}$…
We propose a novel compact linear programming (LP) relaxation for binary sub-modular MRF in the context of object segmentation. Our model is obtained by linearizing an $l_1^+$-norm derived from the quadratic programming (QP) form of the MRF…
The max-min fair allocation problem seeks an allocation of resources to players that maximizes the minimum total value obtained by any player. Each player $p$ has a non-negative value $v_{pr}$ on resource $r$. In the restricted case, we…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
This paper presents a canonical duality approach for solving a general topology optimization problem of nonlinear elastic structures. By using finite element method, this most challenging problem can be formulated as a mixed integer…
In recent years, linear complementary pairs (LCP) of codes and linear complementary dual (LCD) codes have gained significant attention due to their applications in coding theory and cryptography. In this work, we construct explicit LCPs of…
We introduce a new two-sided type system for verifying the correctness and incorrectness of functional programs with atoms and pattern matching. A key idea in the work is that types should range over sets of normal forms, rather than sets…
Various first order approaches have been proposed in the literature to solve Linear Programming (LP) problems, recently leading to practically efficient solvers for large-scale LPs. From a theoretical perspective, linear convergence rates…
The linear programming (LP) approach has a long history in the theory of approximate dynamic programming. When it comes to computation, however, the LP approach often suffers from poor scalability. In this work, we introduce a relaxed…