MSc Physics (Electronics I) SEM I 2022 2023 Jan 2023 ALGORITHMS FOR OPTIMIZATION Question Paper - Mumbai University | munotes

Questions asked in this paper

• (2) Figures to the right indicate full marks

1. Q1 Attempt any two of the following 12 marks
   • a) Explain the role of a designer in the optimization process 6
   • b) What are critical points? Explain its importance to find local minimizer. 6 Golden section search uses the golden ratio to approximate Fibonacci 6 search. Thus, explain Fibonacci and golden section search on a unimodal function
   • d) Give an example of a nontrivial function where quadratic fit search 6 would identify the minimum correctly once the function values at three distinct points are available
2. Q2 Attempt any two of the following 12 marks
   • a) Prove that d“*” and are orthogonal using gradient decent 6
   • b) State the first order methods. Thus explain Adagrad method 6
   • c) Explain Secant Method in detail. 6
   • d) When finding roots in one dimension, when would we use Newton’s 6 method instead of the bisection method?
3. Q3 Attempt any two of the following 12 marks
   • a) Explain how to calculate pairwise distance between point in sampling 6
   • b) What is the use of Quasi-Random Sequences? Thus state the quasi- 6 Monte Carlo method’s error convergence as compared to Monte Carlo What is the use of Holdout method? Explain 6
   • d) Explain the linear models in detail. 6
4. Q4 Attempt any two of the following 12 marks
   • a) What are different types of uncertainty explain any three. 6 In the explain two inferences of the coefficients Thus visualize the Orthogonal basis functions for uniform, exponential, and unit Gaussian distributions What is dynamic programming? Explain 6
   • d) Explain Ant Colony optimization as an optimal approach for solving 6 Paper Subject Code: 94744 Computer Science: Algorithms for Optimization (R-2021-22)
5. Q5 Attempt any two of the following 12 marks
   • a) What is Unimodality? Explain. 6
   • b) Explain the working of, RMSProp. And thus explain its advantages over 6 Explain how Greedy local search and the exchange algorithm can be 6 used to find a subset of points that maximally fill a space
   • d) When would we use a more descriptive model, for example, with 6

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