相关论文: Tropical pseudolinear and pseudoquadratic optimiza…
We discuss the tropical analogues of several basic questions of convex duality. In particular, the polar of a tropical polyhedral cone represents the set of linear inequalities that its elements satisfy. We characterize the extreme rays of…
This article examines mean-field-type game problems by means of a direct method. We provide various solvable examples beyond the classical linear-quadratic game problems. These include quadratic-quadratic games and games with power,…
Already for bivariate tropical polynomials, factorization is an NP-Complete problem. In this paper, we give an efficient algorithm for factorization and rational factorization of a rich class of tropical polynomials in $n$ variables.…
The optimal value computation for turned-based stochastic games with reachability objectives, also known as simple stochastic games, is one of the few problems in $NP \cap coNP$ which are not known to be in $P$. However, there are some…
A new multidimensional optimization problem is considered in the tropical mathematics setting. The problem is to minimize a nonlinear function defined on a finite-dimensional semimodule over an idempotent semifield and given by a conjugate…
We establish that the subgame perfect equilibrium (SPE) threshold problem for mean-payoff games is NP-complete. While the SPE threshold problem was recently shown to be decidable (in doubly exponential time) and NP-hard, its exact worst…
In the last few years there has been a growing interest towards methods for statistical inference and learning based on computational geometry and, notably, tropical geometry, that is, the study of algebraic varieties over the min-plus…
We consider constrained linear-quadratic dynamic games arising in autonomous vehicle platooning, intersection crossing and other cooperative driving scenarios. Infinite-horizon Nash equilibria are reformulated as receding-horizon affine…
In this paper, we propose two iterative methods for finding a common solution of a finite family of equilibrium problems for pseudomonotone bifunctions. The first is a parallel hybrid extragradient-cutting algorithm which is extended from…
We apply methods and techniques of tropical optimization to develop a new theoretical and computational framework for the implementation of the Analytic Hierarchy Process in multi-criteria problems of rating alternatives from pairwise…
We study the existence of classical solutions to a broad class of local, first order, forward-backward Extended Mean Field Games systems, that includes standard Mean Field Games, Mean Field Games with congestion, and mean field type control…
We consider decision problems of rating alternatives based on their pairwise comparisons according to two criteria. Given pairwise comparison matrices for each criterion, the problem is to find the overall scores of the alternatives. We…
We introduce the notion of linearly representable games. Broadly speaking, these are TU games that can be described by as many parameters as the number of players, like weighted voting games, airport games, or bankruptcy games. We show that…
The algebraic foundation of tropical polynomial algebra provides the framework for the geometric construction of the supplement and the reversal of tropical varieties, thereby inducing a duality of reduced tropical varieties; for classes of…
We consider some well-known families of two-player, zero-sum, perfect information games that can be viewed as special cases of Shapley's stochastic games. We show that the following tasks are polynomial time equivalent: - Solving simple…
In this paper, we present methods for solving a system of linear equations, $ AX=b $, over tropical semirings. To this end, if possible, we first reduce the order of the system through some row-column analysis, and obtain a new system with…
The connection between game theory, convex optimization, and geometry is deep. There are many applications of linear programming methods and polyhedral representation conversion methods in game theory. In this paper, we discuss two more…
We consider two-player games played on weighted directed graphs with mean-payoff and total-payoff objectives, two classical quantitative objectives. While for single-dimensional games the complexity and memory bounds for both objectives…
This short note establishes positionality of mean-payoff games over infinite game graphs by constructing a well-founded monotone universal graph.
A tropical (or min-plus) semiring is a set $\mathbb{Z}$ (or $\mathbb{Z \cup \{\infty\}}$) endowed with two operations: $\oplus$, which is just usual minimum, and $\odot$, which is usual addition. In tropical algebra the vector $x$ is a…