6 votes
Accepted

Single KKT solution for a simple problem: proof of being minimizer

You have shown that KKT is necessary for a local minimum. Also that it is necessary for a local maximum. But you have not shown that a local minimum or local maximum exists. Indeed, there is no local ...
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4 votes
Accepted

Radial unboundedness vs convexity

The notation $C^1$ means $f'$ is continuous (on $\Bbb R$ as the interval is not stated). In general $C^k(a,b]$ means that all of $f',f'',\cdots,f^{(k)}$ are continuous on $(a,b]$. You are correct ...
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  • 5,010
2 votes

Quality of Solutions from Saddle Points vs. Local Minimums

In minimization a lower loss if preferable under all circumstances. Each saddle point has a local minima one could discover from it if one walked in the right direction. Whether an individual saddle ...
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1 vote
Accepted

Large MINLP problem, searching for solver, tried BARON, ANTIGONE, DICOPT

If a deterministic global optimisation solver (such as Baron) reports a local solution, that solution is reliable. If the solver is terminated prematurely, the global solver will return the best ...
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