Can the YALMP optimize two variables? For example, alpha>0 and beta>0 (I want alpha is as large as possible and beta is as small as possible).

[Harvey]

Dear:

I always use YALMIP to minimize a variable, for example:

optimize(LMIs,beta,options);  % (the variable "beta" can be minimized).  LMIs denotes the LMI conditions. the solvers can be sdpt3, sedumi, mosek. 

I have two questions. My first question is: Can the YALMIP maximize a variable?

My second question is: Can the YALMP optimize two variables? For example, alpha>0 and beta>0 (I want alpha is as large as possible and beta is as small as possible).

Many thanks in advance!

[Piotr Balik]

Hello!

I think you should let objective function become -alpha^2+beta^2 so then the bigger alpha gets the lower value is. You could change the expressions of the values e.g. obj=-alpha^3+beta etc.

About the constrains: just put F = [F, alpha>=0, beta>=0]

Warm regards

[Johan Löfberg]

You would have to define what you actually mean with "optimize two variables". If you are talking about multi-objective optimization, 

https://yalmip.github.io/multiobjective

to maximize an expression, you simply minimize the negated expression

[Johan Löfberg]

Using -alpha^2 + beta^2 (or -beta^3) would be a horrible choice when trying to scalarize a multi-objective, as it would give you a nonconvex objective