Numerical simulation in fluid dynamics: a practical introduction
Numerical simulation in fluid dynamics: a practical introduction
A Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm Pseudospectra
SIAM Journal on Matrix Analysis and Applications
Frame based methods for unconstrained optimization
Journal of Optimization Theory and Applications
On the Convergence of Pattern Search Algorithms
SIAM Journal on Optimization
Pattern Search Algorithms for Bound Constrained Minimization
SIAM Journal on Optimization
Pattern Search Methods for Linearly Constrained Minimization
SIAM Journal on Optimization
Curvature Based Image Registration
Journal of Mathematical Imaging and Vision
Analysis of Generalized Pattern Searches
SIAM Journal on Optimization
A Pattern Search Filter Method for Nonlinear Programming without Derivatives
SIAM Journal on Optimization
Second-Order Behavior of Pattern Search
SIAM Journal on Optimization
Mesh Adaptive Direct Search Algorithms for Constrained Optimization
SIAM Journal on Optimization
Convergence of Mesh Adaptive Direct Search to Second-Order Stationary Points
SIAM Journal on Optimization
OrthoMADS: A Deterministic MADS Instance with Orthogonal Directions
SIAM Journal on Optimization
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In this paper, we characterize a new class of computationally expensive optimization problems and introduce an approach for solving them. In this class of problems, objective function values may be directly related to the computational time required to obtain them, so that, as the optimal solution is approached, the computational time required to evaluate the objective is significantly less than at points farther away from the solution. This is motivated by an application in which each objective function evaluation requires both a numerical fluid dynamics simulation and an image registration process, and the goal is to find the parameter values of a predetermined reference image by comparing the flow dynamics from the numerical simulation and the reference image through the image comparison process. In designing an approach to numerically solve the more general class of problems in an efficient way, we make use of surrogates based on CPU times of previously evaluated points, rather than their function values, all within the search step framework of mesh adaptive direct search algorithms. Because of the expected positive correlation between function values and their CPU times, a time cutoff parameter is added to the objective function evaluation to allow its termination during the comparison process if the computational time exceeds a specified threshold. The approach was tested using the NOMADm and DACE MATLAB® software packages, and results are presented.