Questions tagged [local-minimum]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0 votes
0 answers

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 ...
Nada.S's user avatar
  • 409
2 votes
1 answer

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 ...
not_sure95's user avatar
0 votes
0 answers

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 ...
Javidit's user avatar
  • 53
2 votes
2 answers

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} (\...
JEK's user avatar
  • 121
1 vote
1 answer

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 ...
stats_noob's user avatar
  • 1,821
2 votes
1 answer

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 ...
Devon Elizabeth's user avatar
3 votes
1 answer

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: $...
independentvariable's user avatar
5 votes
1 answer

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^*...
independentvariable's user avatar