相关论文: Matrix Games, Linear Programming, and Linear Appro…

This paper provides the first meaningful documentation and analysis of an established technique which aims to obtain an approximate solution to linear programming problems prior to applying the primal simplex method. The underlying…

This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…

A risk-aware decision-making problem can be formulated as a chance-constrained linear program in probability measure space. Chance-constrained linear program in probability measure space is intractable, and no numerical method exists to…

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…

Floor planning is an important and difficult task in architecture. When planning office buildings, rooms that belong to the same organisational unit should be placed close to each other. This leads to the following NP-hard mathematical…

We exhibit a class of classical or tropical posynomial systems which can be solved by reduction to linear or convex programming problems. This relies on a notion of colorful vectors with respect to a collection of Newton polytopes. This…

We discuss four famous card games that can help learn linear algebra. The games are: SET, Socks, Spot it!, and EvenQuads. We describe the game in the language of vector, affine, and projective spaces. We also show how these games are…

Effective matrix methods for solving standard linear algebra problems in a commutative domains are discussed. Two of them are new. There are a methods for computing adjoined matrices and solving system of linear equations in a commutative…

Nonlinear matrix equations arise in many practical contexts related to control theory, dynamical programming and finite element methods for solving some partial differential equations. In most of these applications, it is needed to compute…

We had assembled a Java package, known as MatrixPak, of four classes for the purpose of numerical matrix computation. The classes are matrix, matrix_operations, StrToMatrix, and MatrixToStr; all of which are inherited from java.lang.Object…

Solving parity games is a major building block for numerous applications in reactive program verification and synthesis. While they can be solved efficiently in practice, no known approach has a polynomial worst-case runtime complexity. We…

We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…

We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…

This is an exercise based approach to matrix groups. The idea is to collect a bunch of exercises at one place which anyone with basic knowledge of linear algebra can attempt to solve and learn matrix groups and algebraic groups.

We establish a linear programming formulation for the solution of joint chance constrained optimal control problems over finite time horizons. The joint chance constraint may represent an invariance, reachability or reach-avoid…

While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the constraints that optimal solutions need to satisfy, and…

Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…

Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…

There has been a recent push in making machine learning models more interpretable so that their performance can be trusted. Although successful, these methods have mostly focused on the deep learning methods while the fundamental…

This article presents an overview of applications of logic programming, classifying them based on the abstractions and implementations of logic languages that support the applications. The three key abstractions are join, recursion, and…