There is a convex program with the convex constraint:
sup_{V \in \math{V}}Tr(QV)+\sum_{i=1}^{d}sup_{P_i \in \math{P_i}}Integral of max{p_i*Ksi_i^2+2q_i*Ksi_i+r_i, p_i' *Ksi_i^2 + 2q_i' *Ksi_i + r_i'}dP_i
That depends in what area is this method. Definetely I'm not interested in complete enumeration, outlining on references on practical methods would help.
It seems that, if the suprema are efficiently computable, we can sample a stochastic subgradient for the left-hand-side of the constraint. Then, one can use a variant of Stochastic Mirror Descent from https://arxiv.org/pdf/1705.02031.pdf
If it is not efficiently computable? The approach will be the same?
Thank you, I will check the reference!
I'm not sure that the same approach will work. To calculate a stochastic subgradient of the sup_{P_i \in \math{P_i}}Integral of max{p_i*Ksi_i^2+2q_i*Ksi_i+r_i, p_i' *Ksi_i^2 + 2q_i' *Ksi_i + r_i'}dP_i we need to know on which P_i the supremum is attained.
Thank you Pavel!
I met this program while reading the info on convex programming and I was interested in general methods of building the effective solutions. I see from your remark that there are these methods. The problem that we have no specialists on convex programming in our institute, this forum is the way to get info from outside. The problems can be really hard just to notice, without advise it can be difficult to get through.
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