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Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
Programming by demonstration has recently gained much attention due to its user-friendly and natural way to transfer human skills to robots. In order to facilitate the learning of multiple demonstrations and meanwhile generalize to new…
We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are…
Vectorial Genetic Programming (Vec-GP) extends GP by allowing vectors as input features along regular, scalar features, using them by applying arithmetic operations component-wise or aggregating vectors into scalars by some aggregation…
Consider the problem of finding an optimal value of some objective functional subject to constraints over numerical domain. This type of problem arises frequently in practical engineering tasks. Nowdays almost all general methods for…
Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…
Automatic code generation for low-dimensional geometric algorithms is capable of producing efficient low-level software code through a high-level geometric domain specific language. Geometric Algebra (GA) is one of the most suitable…
Dimensionality reduction (DR) is an important technique for data exploration and knowledge discovery. However, most of the main DR methods are either linear (e.g., PCA), do not provide an explicit mapping between the original data and its…
This study investigates the potential of Large Language Models (LLMs) for reconstructing and constructing the physical world solely based on textual knowledge. It explores the impact of model performance on spatial understanding abilities.…
This paper considers a general class of iterative optimization algorithms, referred to as linear-optimization-based convex programming (LCP) methods, for solving large-scale convex programming (CP) problems. The LCP methods, covering the…
Combinatorial optimization problems (COPs) are an important research topic in various fields. In recent times, there have been many attempts to solve COPs using deep learning-based approaches. We propose a novel neural network model that…
Deep Learning Gaussian Processes (DL-GP) are proposed as a methodology for analyzing (approximating) computer models that produce heteroskedastic and high-dimensional output. Computer simulation models have many areas of applications,…
A class of non-convex optimization problems with DC objective function is studied, where DC stands for being representable as the difference $f=g-h$ of two convex functions $g$ and $h$. In particular, we deal with the special case where one…
Multiobjective stochastic programming is a field well located to tackle problems arising in emergencies, given that uncertainty and multiple objectives are usually present in such problems. A new concept of solution is proposed in this…
Traditional Linear Genetic Programming (LGP) algorithms are based only on the selection mechanism to guide the search. Genetic operators combine or mutate random portions of the individuals, without knowing if the result will lead to a…
This paper investigates the problem of determining a binary-valued function through a sequence of strategically selected queries. The focus is an algorithm called Generalized Binary Search (GBS). GBS is a well-known greedy algorithm for…
A sparse linear programming (SLP) problem is a linear programming problem equipped with a sparsity (or cardinality) constraint, which is nonconvex and discontinuous theoretically and generally NP-hard computationally due to the…
Dimensionality-reduction techniques are a fundamental tool for extracting useful information from high-dimensional data sets. Because secant sets encode manifold geometry, they are a useful tool for designing meaningful data-reduction…
Generalized semi-infinite programs (GSIP) are a class of mathematical optimization problems that generalize semi-infinite programs, which have a finite number of decision variables and infinite constraints. Mitsos et al. (Mitsos and…
A method of Sequential Log-Convex Programming (SLCP) is constructed that exploits the log-convex structure present in many engineering design problems. The mathematical structure of Geometric Programming (GP) is combined with the ability of…