What reliable stable numerical programming approach can be used to solve general nonlinear conic programming (SDP and SOCP)? Is any primal dual approach fine or should we use a decent algorithm like Newton and gradient methods? Altough mixed conic programming techniques exist however is there any numerical package that can implement interior point method without representing one cone by other cone? This may speed up the convergence and decrease the computational burden with respect to representing by a single cone like Semidefinite cones!
CVX packge only support GP, SDP ,SOCP and LP . CVX is a programming language which use sedumi sdpt3 and other cores as optimization. its not design for nonlinear programming.
Yes, CVX is only for solving convex optimization problems. But, the new version of it can solve some integer programming problems, I have not read the new version of it. If you like, you should read it. Or else, as far as I know, there is not exist some reliable stable numerical programming approaches which can be used to solve general nonlinear conic programming. Some existing methods are some special methods, which are not reliable stable for solving general conic programming.
PENNON is a code for genuine nonlinear (and nonconvex) SDP, see http://www.penopt.com and the papers on my website. There's no SOCP module, yet, but as far as I know, no such code exists. PENLAB is a free Matlab version of the code and will be soon downloadable from http://www.nag.co.uk/projects/penlab - at the moment, you can just drop me an email and I'll send you the code. What do you mean by "mixed" - mixed integer or mixing NLP-SOCP-SDP? There's a branch-and-bound code within YALMIP for mixed integer conic optimization; it, however, needs our solver PENMBI.
thank you Michal , i was already familiar with your state of the art PENNON package and your related articles but since it wasn't free of charge, I couldn't examine your package so I was hoping someone can tell me how to write the algorithm so that you have answered my question is really surprising. would inform about when you package will be available free of charge and whats the terms of usage ? actually i am not working for industry and just Voluntary working with a bunch of master students working on a specific signal processing problem.
By mixed conic programming, i mean having multiple different cone inequality as constraints. like a Lorentz cone and semi-definite matrix cone. Since your super expert in this field you may help me to find out the theoretical computational complexity of a mixed conic problem. since most of the paper only compute the order of worst case iteration bound, i should remark that i am not interested in that, i am looking for worst case computational complexity in terms of multiplication (or may addition).
whats your email email address that i can get in touch ?
thank you Erling, but i am not sure MOSEK be free of charge and can handle conic constraints and nonlinearity in the same time !
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