Engineering design optimization- Chapter 11 ( Convex optimization)

11.1 Answer true or false and justify your answer. a. The optimum found through convex optimization is guaran- teed to be the global optimum. b. Cone programming problems are a special case of quadratic programming problems. c. It is sometimes possible to obtain distinct feasible regions in linear optimization. d. A quadratic problem is a problem with a quadratic objective and quadratic constraints. e. A quadratic problem is only convex if the Hessian of the objective function is positive definite. f. Solving a quadratic problem is easy because the solution can be obtained analytically. g. Least squares regression is a type of quadratic programming problem. h. Second-order cone programming problems feature a linear objective and a second-order cone constraint. i. Disciplined convex optimization builds convex problems by using convex differentiable functions. j. It is possible to transform some nonconvex problems into convex ones by using a change of variables, adding slack variables, or reformulating the objective function. k. A geometric program is not convex but can be transformed into an equivalent convex program. 1. Convex optimization algorithms work well as long as a good starting point is provided