Q2: In constrained optimization, which of the following methods is most appropriate for solving problems involving equality constraints? (A) Lagrange Multiplier method (B) Genetic Algorithm (C) Newton’s method (D) Simulated Annealing Answer: (A) Lagrange Multiplier method
Q3: The Simplex method is primarily used for solving which type of optimization problems? (A) Linear programming problems (B) Non-linear programming problems (C) Integer programming problems (D) Dynamic programming problems Answer: (A) Linear programming problems
Q4: In the context of convex optimization, which of the following is true? (A) The feasible region is always non-convex (B) The objective function is always concave (C) Any local minimum is also a global minimum (D) The solution cannot be found using the gradient method Answer: (C) Any local minimum is also a global minimum
Q5: Which of the following methods is typically used for solving optimization problems with a large number of variables and constraints? (A) Linear programming relaxation (B) Interior-point method (C) Newton’s method (D) Branch and Bound method Answer: (B) Interior-point method
Q6: In quadratic programming, the objective function is typically: (A) Linear (B) Convex quadratic (C) Non-convex quadratic (D) Piecewise linear Answer: (B) Convex quadratic
Q7: Which of the following optimization methods is based on the concept of “evolutionary” search to find the optimal solution? (A) Genetic Algorithm (B) Simulated Annealing (C) Particle Swarm Optimization (D) Conjugate Gradient Method Answer: (A) Genetic Algorithm
Q8: Which of the following is a primary advantage of using the Nelder-Mead method for optimization? (A) It is faster than gradient-based methods for large-scale problems (B) It does not require the calculation of gradients (C) It guarantees finding the global minimum (D) It is guaranteed to converge to the optimal solution Answer: (B) It does not require the calculation of gradients
Q9: In the context of optimization with constraints, which of the following is a necessary condition for optimality in non-linear programming? (A) The first-order optimality condition (stationarity condition) (B) The second-order sufficient condition (C) The strong duality theorem (D) The KKT conditions Answer: (D) The KKT conditions
Q10: Which of the following methods is most appropriate for solving combinatorial optimization problems? (A) Branch and Bound method (B) Gradient Descent method (C) Interior-point method (D) Newton’s method Answer: (A) Branch and Bound method