New answers tagged convex-optimization
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Accepted
Can the following problem be solved recursively?
As you actually have lots of multiplication of the variables, using any global solver can lead to the linearization of these terms and finally slow convergence. As an alternative, it would be worth ...
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Convexity of p power of the q norm (0<p<1, q>1)
Assuming $q > 1, 0 <p < 1$, as per the question:
If $x$ is a nonnegative scalar, $f(\mathbf{x})=\|\mathbf{x}\|_q^p$ is concave, not convex.
For non-scalar $x$, $f(\mathbf{x})=\|\mathbf{x}\|_q^...
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Bilinear programming
You can "merge" to a single maximization over all variables.
Then use Gurobi (which can solve bilinear problems such as this to global optimality, given enough time and memory) or a general ...
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0
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Basic question about definition of a convex optimization problem
In practice, it is often the case that you observe constraints of the form "$f_i(x) \leq 0$" rather than "$x \in G$". The former constraint defines a convex set if $f_i$ is convex, ...
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How can I relax the equality constraint in this problem?
In addition to @prubin's answer, another approach, which may be useful when $x$ and $y$ are high-dimensional, is to solve the problem in $(1)$ as a difference-of-convex (DC) program. This approach is ...
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Complexity of the ellipsoid method in general convex problems
The following links refers to application of ellipsoidal algorithms with some variations to NLPs:
Paper by Drs. Rugenstein. E & Kupferschimd.M: presents results showing convergence by ellipsoidal ...
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Accepted
How can I relax the equality constraint in this problem?
Let $g(x)=f(x, \log(1 - \exp(x))).$ Try plotting that to see if it is unimodal and, if so, whether the min is attained in the interior or only approached (infimum) as $x\rightarrow -\infty$ or as $x\...
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