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5 votes
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Global optimizers handling minimization of expressions like $\log{v}+\frac{1}{v}$

Consider the simple problem of maximum likelihood estimation of the variance of a mean zero normal distribution. The expression to be minimised is: $$N \log{v}+\frac{1}{v}\sum_{n=1}^N{b_n^2},$$ where $...
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2 votes
0 answers
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Global optimizers handling minimization of an expression arising from the likelihood of a multivariate normal

I am interested in converting the following optimisation problem into a form that an exponential cone and/or SDP solver such as MOSEK can handle. This is a multivariate version of the question I ...
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  • 269
1 vote
1 answer
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How to transform this problem with logarithmic objective function into an approximated convex optimization problem?

I have an objective function as follows $\underset{x_{m,n}}{\max}\hspace{1mm}\hspace{1mm}\sum_{m=1}^{M}\log_2\left(\frac{\sum_{n=1}^{N}(1-x_{m,n})\omega_{m,n}+z}{\sum_{n=1}^{N}x_{m,n}\omega_{m,n}}\...
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