fmincon lower bound interval

I'm seeking for values 0 or more than 0.1 for example. How can I do this?

[Torsten]

help find

if you seek them in an array or a matrix.

Otherwise, you have to explain your problem in more detail.

[Milena Beneva]

partially discrete constraint like "x(i)=0 or x(i)>=0.1"

Answer 1

[Matt J]

You cannot specify a partially discrete constraint like "x(i)=0 or x(i)>=0.1" on your variables with fmincon.

To handle that with fmincon, you must run a separate fmincon optimization for every possible subset S of non-zero x(i) variables, constraining x(i)>=0.1 for and x(i)=0 for .

An alternative to doing a combinatoric optimization would be to introduce binary variables b(i) and impose the linear inequality constraints,

0<=x(i)

b(i)<=10*x(i)

x(i)<=ub(i)*b(i)

The only x(i)<0.1 which satisfies these constraints is x(i)=0. For this approach, however, you would need a solver that can handle binary-constrained variables, like intlinprog (if your objective and other constraints are linear) or ga.

[Walter Roberson]

You could use ga and nonlinear constraints though. ga and patternsearch should be able to handle discontinuities

[Milena Beneva]

Thanks a lot! I do a portfolio optimization (by min risk) but all of assets from initial asset list take a part in optimized portfolio. It is not normal. Some of assets have weigths below 0.00005. I'm looking to desision how to constraint that solution.

[Matt J]

You could use ga and nonlinear constraints though. ga and patternsearch should be able to handle discontinuities

I 'm less optimistic about that being successful. ga cannot do any prior analysis of nonlinear discontinuous constraints to determine how to distribute the initial population over discontinuous feasible regions.