Related papers: Data loci in algebraic optimization
Probabilistic models often have parameters that can be translated, scaled, permuted, or otherwise transformed without changing the model. These symmetries can lead to strong correlation and multimodality in the posterior distribution over…
We consider optimization problems with uncertain constraints that need to be satisfied probabilistically. When data are available, a common method to obtain feasible solutions for such problems is to impose sampled constraints, following…
This paper considers the hyperparameter optimization problem of mathematical techniques that arise in the numerical solution of differential and integral equations. The well-known approaches grid and random search, in a parallel algorithm…
We propose a computational framework for computing low-rank approximations to the ensemble of solutions of a parametrized system of the form $A(\xi)x(\xi)+g(x(\xi))=b(\xi)$ for multiple parameter values. The central idea is to reinterpret…
In this paper the approach to solving several combinatorial optimization problems using the local search and the genetic algorithm techniques is proposed. Initially this approach was developed in purpose to overcome some difficulties…
An algebraic approach to the maximum likelihood estimation problem is to solve a very structured parameterized polynomial system called likelihood equations that have finitely many complex (real or non-real) solutions. The only solutions…
The class PLS (Polynomial Local Search) captures the complexity of finding a solution that is locally optimal and has proven to be an important concept in the theory of local search. It has been shown that local search versions of various…
The identification of performance-optimizing parameter settings is an important part of the development and application of algorithms. We describe an automatic framework for this algorithm configuration problem. More formally, we provide…
Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to…
A computation method of algebraic local cohomology with parameters, associated with zero-dimensional ideal with parameter, is introduced. This computation method gives us in particular a decomposition of the parameter space depending on the…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
Many mathematical imaging problems are posed as non-convex optimization problems. When numerically tractable global optimization procedures are not available, one is often interested in testing ex post facto whether or not a locally…
We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the…
The following questions are often encountered in system and control theory. Given an algebraic model of a physical process, which variables can be, in theory, deduced from the input-output behavior of an experiment? How many of the…
Fair algorithm evaluation is conditioned on the existence of high-quality benchmark datasets that are non-redundant and are representative of typical optimization scenarios. In this paper, we evaluate three heuristics for selecting diverse…
Probabilistic Logic Programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions…
We introduce several modifications of conic fitting in Geometric algebra for conics by incorporating additional conditions into the optimisation problem. Each of these extra conditions ensure additional geometric properties of a fitted…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
This note further addresses the global optimization problem for max-plus linear systems considered in [Automatica 119 (2020) 109104]. Firstly, the operations between infinity elemens and real numbers involved in the formulas of solving…
Linear-parametric optimization, where multiple objectives are combined into a single objective using linear combinations with parameters as coefficients, has numerous links to other fields in optimization and a wide range of application…