OutputFcn: we defined output function in myOutputFcn, which will display iteration information, structural topology corresponding.We will display iteration information in the OutputFcn. Display: display option is turned off.
GradObj, GradConstr, Hessian, HessFcn: With analytic expressions of the gradients of the objective function, constraints and Hessian of the Lagrange function, the optimization algorithm will execute faster than numerical approximation. The hessian in ‘sqp’ or ‘active-set’ are approximated by the means of BFGS (Quasi-Newtown method). The reason why we choose ‘interior-point’ instead of others is because ‘interior-point’ accepted user-supplied Hessian of the Lagrange function while ‘sqp’ and ‘active-set’ do not allow user to provide hessian. Algorithm: Matlab fmincon has many alogrithms, such as ‘sqp’, ‘active-set’, ‘trust-region-reflective’ and ‘interior-point’. TolX: user-defined terminarion criterion. There are lots of OPTIONS defined for fmincon. Since our constraint (volume constraint) is a function of xPhys instead of design variable x, we will define it in the function m圜onstrFcn. ce will be used in both myObjFcn and myHessianFcn. In line 2, a global variable ce is defined. In this step, we are going to initialize parameters used by Matlab fmincon function. 
Then, DELETE lines 64- 96 (mainly the while loop) in the program. Step.0: Remove Codes from Top3dīefore we get started, please download the Top3d program if you haven’t done so. Note: the line numbers in each step is refer to as the code snippets in each step instead of the top3d program. It constrains six(6) main steps, i.e., Initialize Fmincon, Define Objective function, Hessian, Constraint, Output function and Call fmincon.
#Fmincon nonlinear constraints how to
In this tutorial, you will learn how to use Matlab 1 fmincon function as an optimizer in our 3d topology optimization program.
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