Let $$f(x,y,z)=\sqrt{\frac{1}{3}+2xz-y^2}-x-z,$$ where $$x+y+z\leq 1, \quad x+y\geq 0.7, \quad x\geq 0, \quad y\geq 0, \quad \text{and} \quad z\geq 0.$$
How could I go about maximizing this function? I cannot use Lagrange multipliers since my constraints are inequalities. Any ideas? Thank you in advance.