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Then, invoke the unconstrained minimization routine.Create an M-file that returns the function value (Objective Function).IntroductionUnconstrained MinimizationĜonstrained Minimization Multiobjective OptimizationConclusion Steps Consider the problem of finding a set of values T that solves.IntroductionUnconstrained MinimizationĜonstrained Minimization Multiobjective OptimizationConclusion Unconstrained Minimization Default optimization parameters can be changed through an options structure.Optimization options passed to the routines change optimization parameters.Maximization is achieved by supplying the routines with –f.Most of these optimization routines require the definition of an M-file containing the function, f, to be minimized.Introduction Unconstrained MinimizationĜonstrained Minimization Multiobjective OptimizationConclusion Implementing Opt. Introduction Unconstrained MinimizationĜonstrained Minimization Multiobjective OptimizationConclusion Least-Squares Algorithms Introduction Unconstrained MinimizationĜonstrained Minimization Multiobjective OptimizationConclusion Equation Solving Algorithms Introduction Unconstrained MinimizationĜonstrained Minimization Multiobjective OptimizationConclusion Minimization Algorithm (Cont.)

Introduction Unconstrained MinimizationĜonstrained Minimization Multiobjective OptimizationConclusion Minimization Algorithm Specialized algorithms for large scale problems.Nonlinear systems of equations solving.Nonlinear least squares and curve fitting.Constrained nonlinear optimization, including goal attainment problems, minimax problems, and semi-infinite minimization problems.Is a collection of functions that extend the capability of MATLAB.Introduction Unconstrained MinimizationĜonstrained Minimization Multiobjective OptimizationConclusion Optimization Toolbox Can be linear or nonlinear, explicit or implicit functions Equality Constraints Inequality Constraints Most algorithm require less than!!! Side Constraints Introduction Unconstrained MinimizationĜonstrained Minimization Multiobjective OptimizationConclusion Function Optimization Constraints – Limitation to the design space. is a column vector of design variables, which can affect the performance of the system. For maximization, it is equivalent to minimization of the –ve of the objective function. In a standard problem, we are minimizing the function. Introduction Unconstrained MinimizationĜonstrained Minimization Multiobjective OptimizationConclusion Function Optimization is the objective function, which measure and evaluate the performance of a system. Standard Optimization Problem Subject to: Equality Constraints Inequality Constraints Side Constraints.Optimization concerns the minimization or maximization of functions.Introduction Unconstrained MinimizationĜonstrained Minimization Multiobjective OptimizationConclusion Function Optimization MATLAB Optimization Toolbox Presented by Chin Pei February 28, 2003