Related papers: Bounded Homotopy Path Approach to Find the Solutio…
In this article we establish error bound for linear complementarity problem with $P$-matrix using plus function. We introduce a fundamental quantity associated with a $P$-matrix and show how this quantity is useful in deriving error bounds…
Most existing work focuses on the generalization of KKT for nonsmooth convex optimization problems, but this paper explores a generalized form of Karush-Kuhn-Tucker (KKT) conditions for real continuous optimization problems.
Path finding algorithm addresses problem of finding shortest path from source to destination avoiding obstacles. There exist various search algorithms namely A*, Dijkstra's and ant colony optimization. Unlike most path finding algorithms…
First order shape optimization methods, in general, require a large number of iterations until they reach a locally optimal design. While higher order methods can significantly reduce the number of iterations, they exhibit only local…
A reparametrization (of a continuous path) is given by a surjective weakly increasing self-map of the unit interval. We show that the monoid of reparametrizations (with respect to compositions) can be understood via ``stop-maps'' that allow…
We introduce a new pattern recognition algorithm for track finding in High Energy Physics Experiments based on an extension of the Hough Transform to multiple dimensions. A remarkable property of this algorithm is that the execution time is…
Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of…
Quantum walk is a potent technique for building quantum algorithms. This paper examines the quantum walk search algorithm on complete multipartite graphs with multiple marked vertices, which has not been explored before. Two specific cases…
We introduce a new concept of solution to the KPZ equation which is shown to extend the classical Cole-Hopf solution. This notion provides a factorisation of the Cole-Hopf solution map into a "universal" measurable map from the probability…
In the real-time decision-making and local planning process of autonomous vehicles in dynamic environments, the autonomous driving system may fail to find a reasonable policy or even gets trapped in some situation due to the complexity of…
In this paper, we consider a formulation of nonlinear constrained optimization problems. We reformulate it as a time-varying optimization using continuous-time parametric functions and derive a dynamical system for tracking the optimal…
Trajectory similarity retrieval is an important part of spatiotemporal data mining, however, existing methods have the following limitations: traditional metrics are computationally expensive, while learning-based methods suffer from…
In this paper we propose a method that uses Lagrange multipliers and numerical algebraic geometry to find all critical points, and therefore globally solve, polynomial optimization problems. We design a polyhedral homotopy algorithm that…
A new pattern search method for bound constrained optimization is introduced. The proposed algorithm employs the coordinate directions, in a suitable way, with a nonmonotone line search for accepting the new iterate, without using…
In the present work, a new approach is proposed for finding the analytical solution of population balances. This approach is relying on idea of Homotopy Perturbation Method (HPM). The HPM solves both linear and nonlinear initial and…
We prove in this work that the well-known lasso problem can be solved exactly without homotopy using novel differential inclusions techniques. Specifically, we show that a selection principle from the theory of differential inclusions…
The solution space of any set of power flow equations may contain different number of real-valued solutions. The boundaries that separate these regions are referred to as power flow solution space boundaries. Knowledge of these boundaries…
In this article we develop a general theory of exact parametric penalty functions for constrained optimization problems. The main advantage of the method of parametric penalty functions is the fact that a parametric penalty function can be…
The concept of path homotopy has received widely attention in the field of path planning in recent years. In this article, a homotopy invariant based on convex dissection for a two-dimensional bounded Euclidean space is developed, which can…
For a linear complementarity problem, we present a relaxaiton accelerated two-sweep matrix splitting iteration method. The convergence analysis illustrates that the proposed method converges to the exact solution of the linear…