Farzad Hemmati
Farzad Hemmati, University of British Columbia, Canada
Title: Constrained design optimization using MATLAB & ANSYS: Assessment of accuracy & Hessian matrix assumptions
Biography
Biography: Farzad Hemmati
Abstract
In this paper, a nonlinear constrained optimization problem is solved using MATAB’s Optimization Toolbox and ANSYS APDL’s Design Optimization. The objective is to investigate the accuracy of both methods and to assess the assumptions used in approximating the Hessian matrix in each case. The sequential quadratic programming (SQP) technique is applied through MATLAB and a subproblem approximation method using the sequential unconstrained minimization technique (SUMT) through APDL. SQP linearizes the constraints and solves the QP subproblem to form a line search to decrease the descent function whereas in SUMT the constrained problem is converted to an unconstrained problem using a transformation that applies a penalty function in place of the constraints. Comparing the two techniques it was found, based on the results that the sub problem approximation method from APDL proved more accurate since the optimum solution was a global minimum, whereas in MATLAB a local minimum result was obtained. The treatment of the Hessian matrix by the two techniques was studied in order to understand its effect on the results; the SQP method utilizes a quasi-Newtonian method, the BFGS method, to approximate the Hessian matrix while in APDL, no approximation is made since the subproblem approximation method is a zero-order method.