Constrained Optimization

Work in progress. This note is still being written and incomplete.

Constrained optimization minimizes or maximizes f(x)f(x) subject to restrictions on the design variables xx.

General Form

min⁡xf(x)\min_x f(x)

subject to

gi(x)=ci,i=1,…,ng_i(x) = c_i, \quad i = 1, \ldots, n hj(x)≤dj,j=1,…,mh_j(x) \leq d_j, \quad j = 1, \ldots, m

Here:

  • gi(x)=cig_i(x) = c_i: equality constraints
  • hj(x)≤djh_j(x) \leq d_j: inequality constraints
Written by October 7, 2026 1 min read
Was this helpful?