Problem with exp function

Nonconvex
1

I wanna to solve the following question:

cvx_begin

variable x1

variable x2

variable lambda

minimize (lambda)

subject to

    1-pow_p(2.718281828,-0.7*0.00005*10000*pow_p(x1,-0.3))-0.4*lambda<=0

    1-pow_p(2.718281828,-0.8*0.00007*10000*pow_p(x2,-0.2))-0.4*lambda<=0

    x1+x2-300<=0

    x1>=0

    x2>=0

    lambda>=0

    lambda-1<=0

cvx_end

But the solution for this is x1=126.72, x2=110.84, lambda=9.87*e^-11

which contradict with first and second constraint or

1-pow_p(2.718281828,-0.70.0000510000pow_p(x1,-0.3))-0.4lambda<=0

1-pow_p(2.718281828,-0.80.0000710000pow_p(x2,-0.2))-0.4lambda<=0

So the solution is wrong.

I want to know what is wrong with my code.

2

I’m frankly surprised CVX is even accepting this. I don’t think it should be. The inner pow_p term is concave, so the outer pow_p terms are log-concave, which are very restricted.

3

I don’t think this problem is convex; but even if it were, it’s violating the DCP rules. Did you try exp only to find that it gave you an error? If so there is a bug in pow_p somewhere. But regardless, CVX will not be able to solve this.