Related papers: Reducing Linear Programs into Min-max Problems
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We introduce multiple symmetric LP relaxations for minimum cut problems. The relaxations give optimal and approximate solutions when the input is a Hamiltonian cycle. We show that this leads to one of two interesting results. In one case,…
We introduce two min-max problems: the first problem is to minimize the supremum of finitely many rational functions over a compact basic semi-algebraic set whereas the second problem is a 2-player zero-sum polynomial game in randomized…
Much effort has been directed at algorithms for obtaining the highest probability configuration in a probabilistic random field model known as the maximum a posteriori (MAP) inference problem. In many situations, one could benefit from…
We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are…
This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…
We present a local algorithm (constant-time distributed algorithm) for approximating max-min LPs. The objective is to maximise $\omega$ subject to $Ax \le 1$, $Cx \ge \omega 1$, and $x \ge 0$ for nonnegative matrices $A$ and $C$. The…
Typical behavior of the linear programming problem (LP) is studied as a relaxation of the minimum vertex cover problem, which is a type of the integer programming problem (IP). To deal with the LP and IP by statistical mechanics, a…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…
Our contribution in this paper is two folded. We consider first the case of linear programming with real coefficients and give a method which allows the computation of a new upper bound on the distance from the origin to a feasible point.…
Determining the maximum demand a water distribution network can satisfy is crucial for ensuring reliable supply and planning network expansion. This problem, typically formulated as a mixed-integer nonlinear program (MINLP), is…
Message-passing algorithms based on belief-propagation (BP) are successfully used in many applications including decoding error correcting codes and solving constraint satisfaction and inference problems. BP-based algorithms operate over…
We consider the global minimization of a particular type of minimum structured optimization problems wherein the variables must belong to some basic set, the feasible domain is described by the intersection of a large number of functional…
We present an optimization problem emerging from optimal control theory and situated at the intersection of fractional programming and linear max-min programming on polytopes. A na\"ive solution would require solving four nested, possibly…
This paper considers the problem of maximizing multiple linear functions over the probability simplex. A classification of feasible points is indicated. A necessary and sufficient condition for a member of each class to be an efficient…
In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…
Increasing the complexity of solving budgetary allocation (NP-hardness problem) has led a wide range of methods to minimize the costs. Metaheuristics and Linear Programming (LP) are the most optimization in this fields. Therefore, this…
In this paper we propose a new iterative algorithm to solve the fair PCA (FPCA) problem. We start with the max-min fair PCA formulation originally proposed in [1] and derive a simple and efficient iterative algorithm which is based on the…
It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs). This paper gives a positive answer to this question by…
In this paper, we focus on nonlinear infinite-norm minimization problems that have many applications, especially in computer science and operations research. We set a reliable Lagrangian dual aproach for solving this kind of problems in…