相关论文: Matrix Games, Linear Programming, and Linear Appro…
In this paper we survey the computational time complexity of assorted simple stochastic game problems, and we give an overview of the best known algorithms associated with each problem.
We consider potential games with mixed-integer variables, for which we propose two distributed, proximal-like equilibrium seeking algorithms. Specifically, we focus on two scenarios: i) the underlying game is generalized ordinal and the…
Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation.
In this paper, we study three algorithmic problems involving computation trees: the optimization, solvability, and satisfiability problems. The solvability problem is concerned with recognizing computation trees that solve problems. The…
We give an approximation algorithm for packing and covering linear programs (linear programs with non-negative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm computes feasible primal and dual…
Matching games naturally generalize assignment games, a well-known class of cooperative games. Interest in matching games has grown recently due to some breakthrough results and new applications. This state-of-the-art survey provides an…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint. We show that for any linear program there exists an optimal solution…
Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…
In nearly every discipline, scientific computations are limited by the cost and speed of computation. For example, the best-known exact algorithms for the canonical Traveling Salesman Problem would take centuries to run on an instance of…
Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…
Partial-monitoring games constitute a mathematical framework for sequential decision making problems with imperfect feedback: The learner repeatedly chooses an action, opponent responds with an outcome, and then the learner suffers a loss…
We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…
We use matrix iteration theory to characterize acceleration in smooth games. We define the spectral shape of a family of games as the set containing all eigenvalues of the Jacobians of standard gradient dynamics in the family. Shapes…
Round robin tournaments are omnipresent in sport competitions and beyond. We propose two new integer programming formulations for scheduling a round robin tournament, one of which we call the matching formulation. We analytically compare…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
We show that the linear or quadratic 0/1 program\[P:\quad\min\{ c^Tx+x^TFx : \:A\,x =b;\:x\in\{0,1\}^n\},\]can be formulated as a MAX-CUT problem whose associated graph is simply related to the matrices $\F$ and $\A^T\A$.Hence the whole…
We refine a model for linear logic based on two well-known ingredients: games and simulations. We have already shown that usual simulation relations form a sound notion of morphism between games; and that we can interpret all linear logic…
We present an approximation scheme for optimizing certain Quadratic Integer Programming problems with positive semidefinite objective functions and global linear constraints. This framework includes well known graph problems such as Minimum…
We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…
In this work, we state a general conjecture on the solvability of optimization problems via algorithms with linear convergence guarantees. We make a first step towards examining its correctness by fully characterizing the problems that are…