scholarly journals Second-Order Shape Optimization for Geometric Inverse Problems in Vision

2014 ◽  
Author(s):  
Jonathan Balzer ◽  
Stefano Soatto
Keyword(s):  
Inverse Problems ◽  
Shape Optimization ◽  
Second Order ◽  
Geometric Inverse Problems

Development of an Optimization Framework for Parameter Identification and Shape Optimization Problems in Engineering

2011 ◽  
Vol 1 (1) ◽  
pp. 57-79 ◽  
Author(s):  
A. Andrade-Campos
Keyword(s):  
Inverse Problems ◽  
Shape Optimization ◽  
Parameter Identification ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimum Shape ◽  
Optimization Framework ◽  
Search Optimization ◽  
Initial Geometry

The use of optimization methods in engineering is increasing. Process and product optimization, inverse problems, shape optimization, and topology optimization are frequent problems both in industry and science communities. In this paper, an optimization framework for engineering inverse problems such as the parameter identification and the shape optimization problems is presented. It inherits the large experience gain in such problems by the SiDoLo code and adds the latest developments in direct search optimization algorithms. User subroutines in Sdl allow the program to be customized for particular applications. Several applications in parameter identification and shape optimization topics using Sdl Lab are presented. The use of commercial and non-commercial (in-house) Finite Element Method codes to evaluate the objective function can be achieved using the interfaces pre-developed in Sdl Lab. The shape optimization problem of the determination of the initial geometry of a blank on a deep drawing square cup problem is analysed and discussed. The main goal of this problem is to determine the optimum shape of the initial blank in order to save latter trimming operations and costs.

scholarly journals On some geometric inverse problems for nonscalar elliptic systems

2020 ◽  
Vol 269 (11) ◽  
pp. 9123-9143
Author(s):  
Raul K.C. Araújo ◽  
Enrique Fernández-Cara ◽  
Diego A. Souza
Keyword(s):  
Inverse Problems ◽  
Elliptic Systems ◽  
Geometric Inverse Problems

A Second Order Approximation Technique for Robust Shape Optimization

2011 ◽  
Vol 104 ◽  
pp. 13-22 ◽  
Author(s):  
Adrian Sichau ◽  
Stefan Ulbrich
Keyword(s):  
Shape Optimization ◽  
Order Approximation ◽  
Trust Region ◽  
State Equation ◽  
Second Order ◽  
Approximation Technique ◽  
Worst Case ◽  
Second Order Approximation ◽  
Robust Counterpart ◽  
Adjoint Approach

We present a second order approximation for the robust counterpart of general uncertain nonlinear programs with state equation given by a partial di erential equation.We show how the approximated worst-case functions, which are the essential part of the approximated robust counterpart, can be formulated as trust-region problems that can be solved effciently using adjoint techniques. Further, we describe how the gradients of the worst-case functions can be computed analytically combining a sensitivity and an adjoint approach. This methodis applied to shape optimization in structural mechanics in order to obtain optimal solutions that are robust with respect to uncertainty in acting forces. Numerical results are presented.

scholarly journals Some geometric inverse problems for the linear wave equation

2015 ◽  
Vol 9 (2) ◽  
pp. 371-393 ◽  
Author(s):  
Anna Doubova ◽  
◽  
Enrique Fernández-Cara
Keyword(s):  
Wave Equation ◽  
Inverse Problems ◽  
Linear Wave ◽  
Linear Wave Equation ◽  
Geometric Inverse Problems

scholarly journals On the Second-Order Shape Derivative of the Kohn-Vogelius Objective Functional Using the Velocity Method

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Jerico B. Bacani ◽  
Julius Fergy T. Rabago
Keyword(s):  
Free Boundary ◽  
Shape Optimization ◽  
Optimization Technique ◽  
Velocity Fields ◽  
Second Order ◽  
Shape Derivative ◽  
State Variables ◽  
Derivatives Of ◽  
Objective Functional ◽  
Perturbation Of Identity

The exterior Bernoulli free boundary problem was studied via shape optimization technique. The problem was reformulated into the minimization of the so-called Kohn-Vogelius objective functional, where two state variables involved satisfy two boundary value problems, separately. The paper focused on solving the second-order shape derivative of the objective functional using the velocity method with nonautonomous velocity fields. This work confirms the classical results of Delfour and Zolésio in relating shape derivatives of functionals using velocity method and perturbation of identity technique.

scholarly journals Well-posed Bayesian geometric inverse problems arising in subsurface flow

2014 ◽  
Vol 30 (11) ◽  
pp. 114001 ◽  
Author(s):  
Marco A Iglesias ◽  
Kui Lin ◽  
Andrew M Stuart
Keyword(s):  
Inverse Problems ◽  
Subsurface Flow ◽  
Geometric Inverse Problems ◽  
Well Posed
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