1. Constrained optimization problems have:
(A) Only equality constraints
(B) Constraints that the solution must satisfy
(C) Step response only
(D) No constraints at all
2. Unconstrained optimization problems:
(A) Have constraints to satisfy
(B) Do not have constraints
(C) Step response only
(D) Only equality constraints
3. Lagrange multipliers are used in:
(A) Unconstrained optimization
(B) Constrained optimization
(C) Step response only
(D) Load flow only
4. First-order necessary condition for optimum is:
(A) Gradient of objective function equals zero
(B) Step response only
(C) Load current only
(D) Hessian matrix positive definite
5. Second-order condition ensures:
(A) Nature of stationary point (max/min)
(B) Step response only
(C) Only gradient zero
(D) Load flow only
6. Equality constraints are expressed as:
(A) g(x) = 0
(B) Step response only
(C) g(x) ≤ 0
(D) Load flow only
7. Inequality constraints are expressed as:
(A) h(x) = 0
(B) g(x) ≤ 0
(C) Step response only
(D) Load flow only
8. Kuhn-Tucker conditions apply to:
(A) Constrained optimization with inequalities
(B) Step response only
(C) Only unconstrained optimization
(D) Load flow only
9. Objective function in unconstrained optimization can be:
(A) Linear or nonlinear
(B) Step response only
(C) Only linear
(D) Load flow only
10. Gradient descent method is used for:
(A) Unconstrained optimization
(B) Step response only
(C) Constrained optimization
(D) Load flow only
11. Lagrangian function combines:
(A) Objective function and constraints
(B) Step response only
(C) Only gradient
(D) Load flow only
12. Constrained optimization problems require:
(A) Handling equality and/or inequality constraints
(B) Step response only
(C) Only gradient descent
(D) Load flow only
13. Hessian matrix in unconstrained optimization is used to:
(A) Determine concavity or convexity
(B) Step response only
(C) Only gradient zero
(D) Load flow only
14. Penalty function methods help to:
(A) Incorporate constraints into objective function
(B) Step response only
(C) Only unconstrained problems
(D) Load flow only
15. Barrier function methods are used to:
(A) Handle inequality constraints
(B) Step response only
(C) Only equality constraints
(D) Load flow only
16. In unconstrained optimization, stationary points occur when:
(A) Gradient = 0
(B) Step response only
(C) Lagrange multipliers ≠ 0
(D) Load flow only
17. For constrained optimization, the gradient of Lagrangian should be:
(A) Zero at optimum
(B) Step response only
(C) Only load current
(D) Load flow only
18. Active constraints are those:
(A) That hold as equalities at optimum
(B) Step response only
(C) Only inequalities
(D) Load flow only
19. In unconstrained optimization, the optimum may be:
(A) Maximum, minimum, or saddle point
(B) Step response only
(C) Only minimum
(D) Load flow only
20. Penalty factor in constrained optimization:
(A) Penalizes violation of constraints
(B) Step response only
(C) Only load flow
(D) Measures voltage only
21. Sequential quadratic programming (SQP) is used for:
(A) Nonlinear constrained optimization
(B) Step response only
(C) Unconstrained linear problems
(D) Load flow only
22. Gradient projection method is applied to:
(A) Constrained optimization
(B) Step response only
(C) Only unconstrained problems
(D) Load flow only
23. In constrained optimization, Lagrange multipliers indicate:
(A) Sensitivity of optimum to constraint changes
(B) Step response only
(C) Only objective function value
(D) Load flow only
24. Barrier methods add a term to:
(A) Penalize approach to constraint boundary
(B) Step response only
(C) Only equality constraints
(D) Load flow only
25. Unconstrained optimization algorithms include:
(A) Gradient descent, Newton-Raphson
(B) Step response only
(C) Only Lagrange multipliers
(D) Load flow only
26. Constrained optimization algorithms include:
(A) Penalty, barrier, SQP methods
(B) Step response only
(C) Only gradient descent
(D) Load flow only
27. Feasible region in constrained optimization is:
(A) Set of points satisfying all constraints
(B) Step response only
(C) Only single point
(D) Load flow only
28. Stationary point in unconstrained optimization:
(A) Gradient = 0
(B) Step response only
(C) Only Hessian positive definite
(D) Load flow only
29. Active set methods identify:
(A) Constraints active at optimum
(B) Step response only
(C) Only unconstrained variables
(D) Load flow only
30. Constrained and unconstrained optimization is widely used in EE for:
(A) Economic dispatch, network optimization, and design problems
(B) Step response only
(C) Load flow only
(D) RMS voltage measurement