Approaching multiple optimization problems

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I am currently looking at solving an optimization problem of the form

$min\ f(arg\max\limits_{k}\quad\max\limits_{\theta} g(k,\theta,t))$

I would really appreciate some guidance in algorithms to solve such problems. The function g is the viterbi state sequence $g(\theta) = p(\text{state seq}=\theta | observation)$

The function f is a mapping from state sequences such that

$f = \sum_{k=0}^{k=\frac{T}{100}}\sum_{t=100k}^{t=100k+100} I(state_t \neq state_{t-1})$

This should in essence minimize the number of state transitions in the most likely sequence.