shargus / constrained-optimization-homework

Constrained optimization homework for the Numerical Optimization exam

Constrained Optimization Homework

Constrained optimization homework for the Numerical Optimization exam.

Text of the problem: consider the following constrained optimization problem, with a hyper-ellipsoid objective function:

$$f(\mathbf{x}) = \sum_{i=1}^{n} x_i^2, \qquad −5.12 \leq x_i \leq 5.12$$

Use your own implementation of the projected gradient method to solve the problem with $n = 10^d$ and $d = 3, 4, 5$, both using exact derivatives and finite differences to approximate the gradient. Compare the behavior of the two implementations, using the following values for the increment $h$:

$$h = 10^{-k}\parallel\hat{\mathbf{x}}\parallel, \qquad k = 2, 4, 6, 8, 10, 12$$

where $\hat{\mathbf{x}}$ is the point at which the derivatives have to be approximated.

User guide

• constr_steepest_desc_bcktrck.m: MatLab function for applying the projected gradient descent method to a function
• constrained_bcktrck_test.m: main code for solving the homework
• CO_report.pdf: report of the homework \w results