Related papers: Tropical optimization techniques in multi-criteria…

Inspired by numerical homotopy methods we propose a combinatorial homotopy algorithm for finding all isolated solutions to a tropical polynomial systems of n tropical polynomials in n variables. In particular, a tropicalisation of the…

New algorithms are proposed for the Tucker approximation of a 3-tensor, that access it using only the tensor-by-vector-by-vector multiplication subroutine. In the matrix case, Krylov methods are methods of choice to approximate the dominant…

Multi-criteria decision support systems are used in various fields of human activities. In every alternative multi-criteria decision making problem can be represented by a set of properties or constraints. The properties can be qualitative…

Operations research applications often pose multicriteria problems. Mathematical research on multicriteria problems predominantly revolves around the set of Pareto optimal solutions, while in practice, methods that output a single solution…

Preference optimization methods have been successfully applied to improve not only the alignment of large language models (LLMs) with human values, but also specific natural language tasks such as summarization and stylistic continuations.…

Trajectory optimization methods for motion planning attempt to generate trajectories that minimize a suitable objective function. Such methods efficiently find solutions even for high degree-of-freedom robots. However, a globally optimal…

Metaheuristic algorithms are essential for solving complex optimization problems in different fields. However, the difficulty in comparing and rating these algorithms remains due to the wide range of performance metrics and problem…

The importance of hierarchically structured representations for tractable planning has long been acknowledged. However, the questions of how people discover such abstractions and how to define a set of optimal abstractions remain open. This…

This study proposes a new constraint handling technique for assisting metaheuristic optimization algorithms to solve constrained optimization problems more effectively and efficiently. Given any two solutions of any constrained optimization…

We propose a hierarchical architecture for efficiently computing high-quality solutions to structured mixed-integer programs (MIPs). To reduce computational effort, our approach decouples the original problem into a higher level problem and…

We construct a soft thresholding operation for rank reduction of hierarchical tensors and subsequently consider its use in iterative thresholding methods, in particular for the solution of discretized high-dimensional elliptic problems. The…

Gradient-based methods are widely used to solve various optimization problems, however, they are either constrained by local optima dilemmas, simple convex constraints, and continuous differentiability requirements, or limited to…

In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…

In this paper, we introduce and analyze a normalization method for solving a system of linear equations over tropical semirings. We use a normalization method to construct an associated normalized matrix, which gives a technique for solving…

In the context of Markov decision processes running in continuous time, one of the most intriguing challenges is the efficient approximation of finite horizon reachability objectives. A multitude of sophisticated model checking algorithms…

We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…

Stochastic optimization algorithms have been successfully applied in several domains to find optimal solutions. Because of the ever-growing complexity of the integrated systems, novel stochastic algorithms are being proposed, which makes…

Design of recommender systems aimed at achieving high prediction accuracy is a widely researched area. However, several studies have suggested the need for diversified recommendations, with acceptable level of accuracy, to avoid monotony…

We introduce a novel approach to portfolio optimization that leverages hierarchical graph structures and the Schur complement method to systematically reduce computational complexity while preserving full covariance information. Inspired by…

We develop a number of general techniques for comparing analytifications and tropicalizations of algebraic varieties. Our basic results include a projection formula for tropical multiplicities and a generalization of the Sturmfels-Tevelev…