A new approach for the effective computation of geodesic regression curves in shape spaces is presented. Here, one asks for a geodesic curve on the shape manifold that minimizes a sum of dissimilarity measures between given twoor three-dimensional input shapes and corresponding shapes along the regression curve. The proposed method is based on a variational time discretization of geodesics. Cur...

In this paper we describe the efficient solution of a PDE-constrained optimization problem subject to the time-periodic heat equation. We propose a space-time formulation for which we develop a monolithic solver. We present preconditioners well suited to approximate the Schur-complement of the saddle point system associated with the first order conditions. This means that in addition to a Richa...

trajectories generally used to describe the space and time required to perform a desired motion task for a mobile robot or manipulator system. in this paper, we considered a cubic polynomial trajectory for the problem of moving a mobile robot from its initial position to a goal position in over a continuous set of time. along the path, the robot requires to observe a certain acceleration profil...

we establish a relationship between general constrained pseudoconvex optimization problems and globally projected dynamical systems. a corresponding novel neural network model, which is globally convergent and stable in the sense of lyapunov, is proposed. both theoretical and numerical approaches are considered. numerical simulations for three constrained nonlinear optimization problems are giv...

Abstract A class of risk-neutral generalized Nash equilibrium problems is introduced in which the feasible strategy set each player subject to a common linear elliptic partial differential equation with random inputs. In addition, player’s actions are taken from bounded, closed, and convex on individual strategies bound constraint state variable. Existence equilibria first-order optimality cond...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 30 June 2020Accepted: 2021Published online: 20 September 2021Keywordsinverse problems, PDE-constrained optimization, extended sources, full waveform inversion, trace estimation, low-rank minimizationAMS Subject Headings86A22, 86A15, 65M32, 65N22, 35Q86, 35R30Publication D...

A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newtontype iteration. Instead of a grid-based discrete representation, the unknown w...

We consider shape optimization of Stokes flow in channels where the objective is to design the lateral walls of the channel in such a way that a desired velocity profile is achieved. This amounts to the solution of a PDE constrained optimization problem with the state equation given by the Stokes system and the design variables being the control points of a Bézier curve representation of the la...

This paper describes an implementation of an interior-point algorithm for large-scale nonlinear optimization. It is based on the algorithm proposed by Curtis, Schenk, and Wächter [SIAM J. Sci. Comput., 32 (2010), pp. 3447-3475], a method that possesses global convergence guarantees to first-order stationary points with the novel feature that inexact search direction calculations are allowed in ...