Question

4.132 Answer True or False. 1. A linear inequality constraint always defines a convex feasible region 2. A linear equality constraint always defines a convex feasible region. 3. A nonlinear equality constraint cannot give a convex feasible region. 4. A function is convex if and only if its Hessian is positive definite everywhere. 5. An optimum design problem is convex if all constraints are linear and the cost function is convex. 6. A convex programming problem always has an optimum solution. 7. An optimum solution for a convex programming problem is always unique. 8. A nonconvex programming problem cannot have global optimum solution. 9. For a convex design problem, the Hessian of the cost function must be positive semidefinite everywhere 10. Checking for the convexity of a function can actually identify a domain over which the function may be convex.

Answer 1

1. False

2. False

Explanation - The feasible region will be convex if :-

a. ) Equality constraint f(x) are linear

b.) and inequality constraints g(x) is less than equal to zero.

Both condition should be fulfilled together to get a feasible convex area.