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Re: Optimization problem
Posted:
Dec 5, 1996 10:47 AM


In article <57gjs0$dad@engser1.erg.cuhk.hk>, mcau@ee.cuhk.hk (Au_Yeung_Man_Ching) writes: > Hi, > > I would like to ask some questions: > > (1) Given the following problem, > > min J(q,S) > q,S > > in doing the above problem, we do the > above problem like this: > > min min J(q,S) > q S > > i.e. doing the problem sequentially as two > parallel independent minimization problem. > With a fixed q first, minimize J(q,S) w.r.t. > S to obtain S*. Then, minimize J(q,S*) w.r.t. > q. Finally, get the optimal point(local/global??) > (q*,S*). > > CAN WE DO THE PROBLEM AS DESCRIBED ABOVE?? > IF CANNOT, how can we do? > if J is convex in the joined variable (q,S) this works and is known for a long time (blockwise coordinate descent). the classical book of blum&oettli 'mathematical optimization (or similar title)' which appeared with Springer publisher is a good source. Otherwise you migth try to solve grad_{q,S}J=0 by solving (analytically or numerically) a subsystem for S=S(q) plug this into the remaining equations and solve these for q (But I am afraid that this will not work well globally even if your problem is quite well behaved but nonconvex) hope this helps peter



