Questions tagged [local-minimum]
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4
questions
1
vote
1
answer
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Quality of Solutions from Saddle Points vs. Local Minimums
Can Saddle Points Provide "Better Solutions" to Machine Learning Models Compared to Local Minimums?
The solution to a Machine Learning model (i.e. the final model parameters) are selected by ...
- 1,839
2
votes
1
answer
120
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Large MINLP problem, searching for solver, tried BARON, ANTIGONE, DICOPT
I am working on a MINLP problem and am searching for a solver that works. I have tried ANTIGONE and receive the following "Termination Status: Infeasible Problem." I also tried DICOPT which ...
3
votes
1
answer
177
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Radial unboundedness vs convexity
We have a simple problem, namely minimizing:
$$f(x) = x_1^2 + x_2^2 - x_1.$$
The gradient is $$\nabla f(x) = \begin{bmatrix} 2x_1 - 1 \\ 2x_2 \end{bmatrix},$$
hence the unique stationary point is: $...
- 3,776
5
votes
1
answer
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Single KKT solution for a simple problem: proof of being minimizer
I have a very simple problem:
$$ \begin{align*}
\begin{array}{ll}
\min\limits_{x_1,x_2} & -x_1x_2 \\
\text{s.t.} & x_1 + x_2 - 2 = 0.
\end{array}
\end{align*} $$
The KKT system gives me $x_1^*...
- 3,776