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There has been a recent interest in imitation learning methods that are guaranteed to produce a stabilizing control law with respect to a known system. Work in this area has generally considered linear systems and controllers, for which…
We develop a homotopy-based framework for computing Karush-Kuhn-Tucker (KKT) points of multiobjective optimization problems. The proposed homotopy map continuously deforms an easily solvable system into the KKT conditions associated with…
We study optimal design problems involving variational inequalities with unilateral conditions in the domain and pointwise boundary observation. We use regularizing and penalization tehniques in the setting of the Hamiltonian approach to…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
In this work, an exact solution to a new generalized nonlinear KdV partial differential equations has been investigated using homotopy analysis techniques. The mentioned partial differential equation has been solved using homotopy…
Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability…
We introduce a class of "inverse parametric optimization" problems, in which one is given both a parametric optimization problem and a desired optimal solution; the task is to determine parameter values that lead to the given solution. We…
The study of parameter-dependent partial differential equations (parametric PDEs) with countably many parameters has been actively studied for the last few decades. In particular, it has been well known that a certain type of parametric…
Machine learning algorithms have been used widely in various applications and areas. To fit a machine learning model into different problems, its hyper-parameters must be tuned. Selecting the best hyper-parameter configuration for machine…
To address the problem of 3D point matching where the poses of two point sets are unknown, we adapt a recently proposed path following based method to use similarity transformation instead of the original affine transformation. The reduced…
This paper is a survey of persistent homology, primarily as it is used in topological data analysis. It includes the theory of persistence modules, as well as stability theorems for persistence barcodes, generalized persistence,…
The stable allocation problem is one of the broadest extensions of the well-known stable marriage problem. In an allocation problem, edges of a bipartite graph have capacities and vertices have quotas to fill. Here we investigate the case…
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…
The survey provides an overview of the developing area of parameterized algorithms for graph modification problems. We concentrate on edge modification problems, where the task is to change a small number of adjacencies in a graph in order…
Parameterization (closure) schemes in numerical weather and climate prediction models account for the effects of physical processes that cannot be resolved explicitly by these models. Methods for finding physical parameterization schemes…
The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
In this article, we apply Homotopy Perturbation Method (HPM) for solving three coupled non-linear equations which play an important role in biosystems. To illustrate the capability and reliability of this method. Numerical example is given…
The homotopy analysis method is studied in the present paper. The question of convergence of the homotopy analysis method is resolved. It is proven that under a special constraint the homotopy analysis method does converge to the exact…
Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…