My problem is I have three equations:
x1^2 - x2^2 + x1 - 3x2 = 2,
x1^3 - x2^4 = -2,
x1^2 + x2^3 + 2x1 - x2 = -1.1
and I want to get the solutions about x1,x2 to minimize the three equations.
But I do not know how to write can satisfy the DCP rulest. HELP HELP
The nonlinear least squares problem formed from these 3 equations is not convex. You should use a nonlinear least squares solver, or could use a smooth unconstrained nonlinear optimization solver.
I arrived at an at least locally optimal solution of x1= -.93176968819226, x2= -1.0461613052289, producing a sum of squares over all 3 equations of 0.000462. The objective function is convex at this solution. I am not guaranteeing there is not a better global optimum. Note that x1= -1,x2= -1 exactly solves the first 2 equations, but results in a larger total sum of squares over the 3 equations of 0.01 (rather than 0.000462) than the solution provided above.
I have got it. Thank you.