Model question

[patwa67]

I just wonder if COSMO can handle a model of the form below:

#Toy data
A = [1.0000 0 0.5000 0.5000 0.4714 0.2357;
    0 1.0000 0.5000 0 0.2357 0.5893;
    0.5000 0 0.2500 1.0000 0.5893 0.2946;
    0.5000 0 0.2500 1.0000 0.5893 0.2946;
    0.4714 0.2357 0.5893 0.5893 1.0000 0.6111;
    0.2357 0.5893 0.5303 0.2946 0.6111 1.0000]

g = [0.5 -0.2 0.3 0.2 0.0 -0.1]
s = [1 0 1 1 0 0]
d = [0 1 0 0 1 1]
F = 0.3

#Model
max c'*g

constr c'*A*c/2 <= F
       c'*s = 0.5
       c'*d = 0.5
       c >= 0

[migarstka]

Hi @patwa67,

If A in your model

#Model
max c'*g

constr c'*A*c/2 <= F
       c'*s = 0.5
       c'*d = 0.5
       c >= 0

is a positive semidefinite matrix then the problem is convex, and you can solve it with COSMO using a second-order-cone constraint.

However, the example matrix that you provided is non-symmetric (positive definiteness is defined for symmetric (or more generally Hermitian) matrices).

Useful references:

• Second order cone constraints in JuMP: https://jump.dev/JuMP.jl/dev/tutorials/conic/tips_and_tricks/#Second-Order-Cone
• Quadratically constrained convex problems
• Lobo, M. S. and Vandenberghe, S. Boyd: Applications of second-order cone programming (1998)