2
votes
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\...
- 37.8k
2
votes
Convex approximation of an expression
No approximation is needed if you wish to minimize the expression. For maximization, see the material after "Edit".
Due to cyclic permutation invariance of trace,
$$\text{trace}(X) = \text{...
- 13.1k
1
vote
Bilinear programming
You can "merge" to a single maximization over all variables.
Then use Gurobi (which can solve bilinear problems such as this to global optimality, given enough time and memory) or a general ...
- 13.1k
1
vote
Convex approximation of an expression with fraction for CVX
I assume the given problem is
$$
\max \frac{\|ax-b\|^2}{\|cx+b\|^2}, x \in \mathbb{C}^N
$$
I may try the following relaxation. The given problem is equivalent to
$$
\begin{align}
&\max &\|ax-...
- 1,036
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