Consider the following non-linear optimization problem: $${min}_c\left(\sum_{i=1}^nc_ix_i-7\right)^2$$
How can we determine the number of local minima points that this optimization problem has?
Is there also a way to find them?
2026-04-13 14:00:19.1776088819
Local minima of a nonlinear optimization problem
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The problem is convex and therefore has a unique minimum value. All $c$ that satisfy $\sum_{i=1}^n c_i x_i=7$ (obtained from setting the derivative to $0$) solve the optimization problem. This is a linear system that has either $0$, $1$ or $\infty$ solutions.