Applied Functional Analysis MCQs

Q1: Which optimization method is best suited for minimizing convex functions subject to inequality constraints? (A) Interior-Point Method (B) Genetic Algorithm (C) Newton-Raphson Method (D) Simplex Method Answer: (A) Interior-Point Method

Q2: In a linear programming problem, the optimal solution lies: (A) At the origin (B) At the centroid of the feasible region (C) At one of the vertices of the feasible region (D) Anywhere in the feasible region Answer: (C) At one of the vertices of the feasible region

Q3: The Kuhn-Tucker (KKT) conditions are used to solve: (A) Linear optimization problems (B) Unconstrained optimization problems (C) Nonlinear constrained optimization problems (D) Quadratic programming problems Answer: (C) Nonlinear constrained optimization problems

Q4: Which of the following optimization methods uses random sampling and probability-based search? (A) Gradient Descent (B) Simplex Method (C) Simulated Annealing (D) Newton’s Method Answer: (C) Simulated Annealing

Q5: The Wolfe conditions are used in: (A) Line search methods for optimization (B) Solving linear equations (C) Nonlinear constraints (D) Gradient-free optimization methods Answer: (A) Line search methods for optimization

Applied Functional Analysis – MCQs with Answers

Q1: The Hahn-Banach theorem guarantees the existence of: (A) A unique linear functional (B) A bounded linear functional on a subspace (C) A compact operator (D) A dual space with finite dimension Answer: (B) A bounded linear functional on a subspace

Q2: The spectrum of a bounded linear operator on a Hilbert space is: (A) Always finite (B) A subset of complex numbers (C) Contained in the real line (D) Equal to the eigenvalues of the operator Answer: (B) A subset of complex numbers

Q3: A Banach space is defined as: (A) A vector space with a bilinear form (B) A complete normed vector space (C) A normed space with an orthonormal basis (D) A space of compact operators Answer: (B) A complete normed vector space

Q4: In functional analysis, a compact operator is: (A) Bounded and has a finite spectrum (B) Linear and has a finite rank (C) A mapping with a compact range (D) Both bounded and maps bounded sets to relatively compact sets Answer: (D) Both bounded and maps bounded sets to relatively compact sets

Q5: The Riesz Representation Theorem applies to: (A) Banach spaces (B) Hilbert spaces (C) Sobolev spaces (D) Compact spaces Answer: (B) Hilbert spaces

Applied Functional Analysis MCQs
By: Prof. Dr. Fazal Rehman | Last updated: November 25, 2024

Applied Functional Analysis – MCQs with Answers

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