Questions tagged [local-minimum]
The local-minimum tag has no usage guidance.
8
questions
0
votes
0
answers
91
views
How should one proceed with column generation when the subproblem generates only columns with positive reduced costs?
I try to solve a MILP with Column generation. The Master Problem is a minimization problem with " $\le$ " constraint which lead to non-positive dual values. The problem is that the ...
- 409
2
votes
1
answer
60
views
Find projection onto implicitly defined set
I think this is a problem a lot of people have in minimization but I couldn't find algorithmic approaches to it.
Given a closed domain $D\subset R^n$ over which a function $f$ is supposed to be ...
- 21
0
votes
0
answers
26
views
Proving Unique Minimum for a Function with Upper Incomplete Gamma Terms
Let $f(t) = 1 + \Gamma(s, a*t) - \Gamma(s, b*t)$ where $\Gamma(.,.)$ represents the upper incomplete gamma function, and $a$ and $b$ and $s$ are positive constants, and $a>b$. Is there a way to ...
- 53
2
votes
2
answers
122
views
Optimize least squares penalized by curvature of log pdf
I have probability values $p \in \mathbb{R}^n$. Given $A \in \mathbb{R}^{m\times n}$, $b \in \mathbb{R}^m$, I want to minimize the following objective function. $||Ap - b||_2^2 + \sum_{i=1}^{n-2} (\...
- 121
1
vote
1
answer
182
views
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 ...
- 1,821
2
votes
1
answer
232
views
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
257
views
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: $...
- 3,970
5
votes
1
answer
545
views
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^*...
- 3,970