Can I perform Second Order Cone Programming in MATLAB 7.8 (R2009a)?

I would like to perform Second Order Cone Optimization in MATLAB.

I would like to know if there are any functions in the optimization toolbox that would perform SOCP.

Answer 1

[MathWorks Support Team]

A problem with a linear objective function and having linear as well as second order cone constraints is called a second order cone programming (SOCP) problem.

A simple type of closed convex pointed cone that captures many optimization problems of interest is the second order cone. Mathematically, this can be represented as:

 x(3)< 10- r,

 where r = x(1)^2 + x(2)^2

A second order cone (SOC) constraint of dimension n specifies that the vector formed by a set of n decision variables must belong to this cone.

SOCP problem can be solved in MATLAB using the interior-point algorithm implemented in the fmincon function. The SOC constraint can be defined as the non-linear constraint.

A similar problem (here the objective function is non-linear) is mentioned in our documentation :

 <http://www.mathworks.com/help/optim/ug/constrained-nonlinear-optimization-examples.html#bri8026>

Answer 2

[Steve Grikschat]

As of R2020b, Optimization Toolbox now has a dedicated solver for second-order cone programming:

https://www.mathworks.com/help//optim/ug/coneprog.html

coupled with a function to make a second-order cone constraint

https://www.mathworks.com/help//optim/ug/optim.coneprog.secondorderconeconstraint.html

For examples see

https://www.mathworks.com/help//optim/ug/cone-programming-mass-nonlinear-spring.html

https://www.mathworks.com/help//optim/ug/convert-quadratic-constraints-to-second-order-cone-constraints.html