Answer true or false: The complex method is similar to the simplex method. The o

Question

Answer true or false: The complex method is similar to the simplex method. The optimum solution of a constrained problem can be the same as the unconstrained optimum. The constraints can introduce local minima in the feasible space. The complex method can handle both equality and inequality constraints. The complex method can be used to solve both convex and nonconvex problems. The number of inequality constraints cannot exceed the number of design variables. The complex method requires a feasible starting point. The solutions of all LP problems in the SLP method lie in the infeasible domain of the original problem. The SLP method is applicable to both convex and nonconvex problems. The usable feasible directions can be generated using random numbers. The usable feasible direction makes an obtuse angle with the gradients of all the constraints. If the starting point is feasible, all subsequent unconstrained minima will be feasible in the exterior penalty function method. The interior penalty function method can be used to find a feasible starting point. The penalty parameter r_k approaches zero as k approaches infinity in the exterior penalty function method. The design vector found through extrapolation can be used as a starting point for the next unconstrained minimization in the interior penalty function method.

Explanation / Answer

7.1

a) True. complex method is a constraint simplex method which uses more points during the search process.

b) False. They are differen. In unconstrained optimization, there are no limitations on the values of the parameters other than that they maximize the value of f. Often, however, there are costs or constraints on these parameters. These constraints make certain points illegal, points that might otherwise be the global optimum.

Constrained optimization problems are generally solved by using mathematical programming approaches like linear programming.

c) True.

d) True. Complex method can handle both equality and inequality constraints.

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