# Questions tagged [local-minimum]

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### 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 ...
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### 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 ...
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### 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 ...
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} (\... 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 ... 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:$...
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^*...