Numerical Analysis in MATLAB

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1. fmincon finds minimum of constrained nonlinear multivariate function. fminunc finds minimum of unconstrained nonlinear multivariate function. fgoalattain solves multiobjective goal attainment problems; fminimax solves minimax constraint problems.

2. When you use one of these functions mentioned above to do optimizations, you might want to pass extra parameters to the objective function. You can do this directly in R, however, you have to this indirectly in MATLAB. To pass extra parameters to the objective function, there are 3 different ways: anonymous function, nested function and global variable. I think anonymous function is the best an most nature way to do it. Suppose you have defined an objective function myObjFun(x,a,b,c), and you want to do optimization for given a, b and c. You can first specify values for a, b and c, define a function handle f=@(x)myObjFun(x,a,b,c), and then optimize function handle f.

3. quadl can be used to numerically calculate integrals. To calculate integrals symbolically, you can use int.