# (x, y) = quad2_min(eps, alpha, beta) # # Sets (x, y) to be the solution to # minimize (x + y)^2 + eps*(x^2 + y^2) + alpha*x + beta*y # subject to x>=0, y>=0 function quad2_min(eps, alpha, beta) x = -((1 + eps) * alpha - beta) / (2 * eps * (2 + eps)); y = -((1 + eps) * beta - alpha) / (2 * eps * (2 + eps)); if ((x < 0) || (y < 0)) if (alpha < beta) x = max(-alpha / (2 * (1 + eps)), 0); y = 0; elseif (alpha > beta) y = max(-beta / (2 * (1 + eps)), 0); x = 0; elseif (alpha == beta) x = max(-alpha / (2 * (2 + eps)), 0); y = max(-alpha / (2* (2 + eps)), 0); end end return (x, y); end