Related papers: Algebraic solutions of tropical optimization probl…
The problem of solving tropical linear systems, a natural problem of tropical mathematics, has already proven to be very interesting from the algorithmic point of view: it is known to be in $NP\cap coNP$ but no polynomial time algorithm is…
In this paper we develop a combinatorial abstraction of tropical linear programming. This generalizes the search for a feasible point of a system of min-plus-inequalities. It is based on the polyhedral properties of triangulations of the…
We show that finding the classical bound of broad families of Bell inequalities can be naturally framed as the contraction of an associated tensor network, but in tropical algebra, where the sum is replaced by the minimum and the product is…
Both unconstrained and constrained minimax single facility location problems are considered in multidimensional space with Chebyshev distance. A new solution approach is proposed within the framework of idempotent algebra to reduce the…
The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining…
We consider the tropical analogues of a particular bilevel optimization problem studied by Dempe and Franke and suggest some methods of solving these new tropical bilevel optimization problems. In particular, it is found that the algorithm…
In this short note, we discuss a goal-oriented multiobjective optimization problem for system performance assessment. The objective function for such optimization problem, which is usually a composite of different performance indices…
The tropical convex hull of a finite set of points in tropical projective space has a natural structure of a cellular free resolution. Therefore, methods from computational commutative algebra can be used to compute tropical convex hulls.…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
We present tropical games, a generalization of combinatorial min-max games based on tropical algebras. Our model breaks the traditional symmetry of rational zero-sum games where players have exactly opposed goals (min vs. max), is more…
Tropical polyhedra seem to play a central role in static analysis of softwares. These tropical geometrical objects play also a central role in parity games especially mean payoff games and energy games. And determining if an initial state…
This is a survey paper on applications of mathematics of semirings to numerical analysis and computing. Concepts of universal algorithm and generic program are discussed. Relations between these concepts and mathematics of semirings are…
We study the interpretation of the lambda-calculus in a framework based on tropical mathematics, and we show that it provides a unifying framework for two well-developed quantitative approaches to program semantics: on the one hand program…
This article focuses on numerical efficiency of projection algorithms for solving linear optimization problems. The theoretical foundation for this approach is provided by the basic result that bounded finite dimensional linear optimization…
This paper is a survey on universal algorithms for solving the matrix Bellman equations over semirings and especially tropical and idempotent semirings. However, original algorithms are also presented. Some applications and software…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
Finding a common factor of two multivariate polynomials with approximate coefficients is a problem in symbolic-numeric computing. Taking a tropical view on this problem leads to efficient preprocessing techniques, applying polyhedral…
We apply an approach based on parametric mean-payoff games to develop bisection and Newton schemes for solving problems of tropical pseudolinear and pseudoquadratic optimisation with general two-sided constraints.