Trust-region methods: Difference between revisions
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Revision as of 01:16, 27 November 2021
Autor: Chun-Yu Chou (cc2398), Ting Guang Yeh (ty262), Yun-Chung Pan (yp392), Chen-Hua Wang (cw893), Fall 2021
Introduction
Problem formulation
Numerical example
Here we will use the trust-region method to solve a classic optimization problem, the Rosenbrock function. The Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is often used as a performance test problem for optimization algorithms. This problem is solved using MATLAB's fminunc as the solver, with 'trust-region' as the solving algorithm.
The function is defined by
The starting point chosen is .
Iteration Process
Iteration 1:
Iterations | f(x) | x | y | Norm of step | First-order optimality |
---|---|---|---|---|---|
1 | 1 | 0.25 | 0 | 1 | 2 |
2 | 0.953125 | 0.263178 | 0.061095 | 0.25 | 12.5 |
3 | 0.549578 | 0.371152 | 0.124076 | 0.0625 | 1.63 |
4 | 0.414158 | 0.539493 | 0.262714 | 0.125 | 2.74 |
5 | 0.292376 | 0.608558 | 0.365573 | 0.218082 | 5.67 |
6 | 0.155502 | 0.765122 | 0.560477 | 0.123894 | 0.954 |
7 | 0.117347 | 0.804353 | 0.645444 | 0.25 | 7.16 |
8 | 0.0385147 | 0.804353 | 0.645444 | 0.093587 | 0.308 |
9 | 0.0385147 | 0.836966 | 0.69876 | 0.284677 | 0.308 |
10 | 0.0268871 | 0.90045 | 0.806439 | 0.0625 | 0.351 |
11 | 0.0118213 | 0.953562 | 0.90646 | 0.125 | 1.38 |
12 | 0.0029522 | 0.983251 | 0.9659 | 0.113247 | 0.983 |
13 | 0.000358233 | 0.99749 | 0.994783 | 0.066442 | 0.313 |
14 | 1.04121e-05 | 0.999902 | 0.999799 | 0.032202 | 0.0759 |
15 | 1.2959e-08 | 1 | 1 | 0.005565 | 0.00213 |
16 | 2.21873e-14 | 1 | 1 | 0.000224 | 3.59E-06 |