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Re: convex optimization problem
Posted:
Aug 24, 2012 5:14 PM


Alan_Weiss <aweiss@mathworks.com> wrote in message <k17tbp$k7a$1@newscl01ah.mathworks.com>... > On 8/24/2012 4:25 AM, kumar vishwajeet wrote: > > Hi, > > I have an objective function of the following type: > > J = x log(x/k) + cx Subject to : f1(x) = alpha and f2(x) = beta > > where alpha, beta, k and c are constants and x is a vector to be > > solved for. So, it is a convex function. Which is the best > > optimization routine in MATLAB to solve such problems. I'm currently > > using fmincon and it is slower than snail. > > > > Thanks. > This is a convex problem only with restrictions on the functions f1 and > f2. I mean, there can be multiple local minima, depending on the > functions f1 and f2. > > But as far as your question goes, the only solver in the toolbox to > handle this type of problem is fmincon. If you are dissatisfied with its > speed, you might want to try some of the suggestions in > http://www.mathworks.com/help/toolbox/optim/ug/br44iv51.html#br44pif > You might also want to try various algorithms, such as sqp. > > Good luck, > > Alan Weiss > MATLAB mathematical toolbox documentation
I'm sorry. The actual cost function is : J = summmation(i = 1:N) (x_i log(x_i/k_i) + c_i*x_i Subject to : x_i >= 0 and summation(i=1:N) (x_i) = 1
where x_i and c_i are scalars. Is it a good idea to change the constraint "x_i >= 0" to "x_i >= eps", where eps is epsilon. I knew that x log x is not defined at x = 0. So I intentionally made x log x = 0 for x = 0. This is valid for maximum entropy problems.



