Related papers: Tropical optimization problems
Optimization networks are a new methodology for holistically solving interrelated problems that have been developed with combinatorial optimization problems in mind. In this contribution we revisit the core principles of optimization…
In this paper, we survey and study definitions and properties of tropical polynomials, tropical rational functions and in general, tropical meromorphic functions, emphasizing practical techniques that can really carry out computations. For…
The tropical rank of a semimodule of rational functions on a metric graph mirrors the concept of rank in linear algebra. Defined in terms of the maximal number of tropically independent elements within the semimodule, this quantity has…
Semiring algebras have been shown to provide a suitable language to formalize many noteworthy combinatorial problems. For instance, the Shortest-Path problem can be seen as a special case of the Algebraic-Path problem when applied to the…
The application of combinatorial optimization problems to solving the problems of planning processes for industries based on a fund of reconfigurable production resources is considered. The results of their solution by mixed integer…
We introduce an alternative approach for constrained mathematical programming problems. It rests on two main aspects: an efficient way to compute optimal solutions for unconstrained problems, and multipliers regarded as variables for a…
An algorithm to give an explicit description of all the solutions to any tropical linear system $A\odot x=B\odot x$ is presented. The given system is converted into a finite (rather small) number $p$ of pairs $(S,T)$ of classical linear…
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…
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…
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…
In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…
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.
We consider the problem of globally minimizing the sum of many rational functions over a given compact semialgebraic set. The number of terms can be large (10 to 100), the degree of each term should be small (up to 10), and the number of…
During the last few years several new results on packing problems were obtained using a blend of tools from semidefinite optimization, polynomial optimization, and harmonic analysis. We survey some of these results and the techniques…
As the development of distributed systems progresses, more and more challenges arise and the need for developing optimized systems and for optimizing existing systems from multiple perspectives becomes more stringent. In this paper I…
There are different solution concepts for convex vector optimization problems (CVOPs) and a recent one, which is motivated from a set optimization point of view, consists of finitely many efficient solutions that generate polyhedral inner…
In this paper, we demonstrate a formulation for optimizing coupled submodular maximization problems with provable sub-optimality bounds. In robotics applications, it is quite common that optimization problems are coupled with one another…
Some results on singularities of plurisubharmonic functions are put into the context of tropical mathematics.
This paper studies approximate solutions of a linear fractional vector optimization problem without requiring boundedness of the constraint set. We establish necessary and sufficient conditions for approximating weakly efficient points of…
We study a bi-objective optimization problem, which for a given positive real number $n$ aims to find a vector $X = \{x_0,\cdots,x_{k-1}\} \in \mathbb{R}^{k}_{\ge 0}$ such that $\sum_{i=0}^{k-1} x_i = n$, minimizing the maximum of $k$…