MA4601/MAT061 Stochastic Search and Optimisation
Assignment 3: Simultaneous Perturbations Due 9:00am Tuesday 17 March, 2020
The task for Assignment 3 is to implement the Adaptive Simultaneous Perturbation (ASP) heuristic, as described in Spall (2003) §7.8. You will need to submit two files: a programme file ti-
tled YOUR NAME programme.r (or .py, .jl, etc.) and a report as a pdf file titled YOUR NAME report.pdf. Submission by email to joneso18@cardiff.ac.uk.
Reference: Spall, J.C. (2003) Introduction to Stochastic Search and Optimization: Estima- tion, Simulation, and Control. John Wiley & Sons, Inc.
Test Problem 1
Use your implementation to find the maximum of the function f(x, y) = sin(x2/2 y2/4) cos(2x ey)
in the region [ 0.5, 3.0]⇥[ 0.5, 2.0], assuming that you can only sample (x, y) ⇠ N(f(x, y), 0.12). Compare the performance of the ASP heuristic to the simultaneous perturbation stochastic
gradient method.
Test Problem 2
Spall (2003) Exercise 7.14.
For x = (x1,…,x10)T 2 (0,1)10 put
f (x) = X ixi + Y 1/xi i=1 i=1
and (x)⇠N(f(x),0.0012(1+P10 x2)). i=1 i
Using independent observations of , estimate that ✓ which minimises f. Compare the performance of the ASP heuristic to the simultaneous perturbation stochastic gradient method.
Marks will be allocated on the following basis: 50% Code correctness and generality.
20% Quality of solutions.
20% Reasoning behind choices for meta-parameters. 10% Clarity of report.
10 10
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