Convex optimization
Convex optimization problem: f(x)->min, where f(x)-convex function, x - point of linspace X, g1(x)=0,...,gm(x)=0, where gi(x)-convex function. Lagrange function: L = l0*f(x)+l1*g1(x)+...+lm*gm(x). See, Kuhn-Tucker theorem. 1) L(xopt,l0_opt,l1_opt,...,lm_opt) = min_x L(l0_opt,l1_opt,...,lm_opt), 2) l0_opt>=0,l1_opt>=0,...,lm_opt>=0 3) l1_opt*g1(xopt)=0, ..., lm_opt*gm(xopt)=0
If l0_opt<>0, so 1)-3) enough to find x_opt
l0_opt<>0, if exist x, so g1(x)<0,...,gm(x)<0.
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