Description
I. (20%): Problem 1.1.4
II. (30%) Problem 1.2.1
III. (50%)
The Mathematics and Computer Science (MCS) Division of the
Argonne National Laboratory is a major research force in
mathematical optimization. They have maintained the NEOS
optimization server and released various high-performance
optimization packages.
Learn how to use them and evaluate several
unconstrained optimization methods in this homework.
1. AMPL (www.ampl.com) is one of the most popular languages for
modeling optimization problems. NEOS (https://neos-server.org/neos/)
is an optimization server that allows users to submit their problems
(in AMPL format and others) to a collection of solvers.
(25%)
a. Study the example AMPL models in
https://www.ampl.com/EXAMPLES/ to learn how to model a
problem in AMPL. Visit the NEOS server, find out the solver
list and how to submit a problem in AMPL to a solver.
b. Download the following three unconstrained problems
dqrtic.mod, eigenbls.mod, freuroth.mod,
from:
https://vanderbei.princeton.edu/ampl/nlmodels/cute/index.html
Submit each of them to the bound constrained solver, L-BFGSB, on NEOS. Report the following:
b.1 Briefly explain the main algorithm of L-BFGS-B.
b.2 Generate a table that lists the solution time (an
estimate will do) and solution quality of the three problems.
2. The Rastrigin Function is a highly nonlinear function with many local
minima. A description of the function can be found at
https://tracer.lcc.uma.es/problems/rastrigin/rastrigin.html. (25%)
a. Write an AMPL model for minimizing the Rastrigin function.
Specify a random non-zero starting point (you can choose
anything you like, such as all x’s = 1.0)
b. Use L-BFGS-B (through NEOS) to solve the Rastrigin problem.
Generate a table that lists the solution time and solution quality, for
n = 10, 20, 50, 100, 1000, 10000. Compare their performance and
discuss your observation. If a solver fails to return a solution for a
problem instance, report “failed” in the table.
Note 1: In your homework report, you only need to provide answers to
Problem 1.1.4, Problem 1.2.1, 1.b, and 2.b.
Note 2: Do not wait until the last day to collect data on the NEOS
server. The NEOS server may get very busy and your job may be queued for
a long time before getting processed.