x = solve_quadratic2(A,c,B,D,seed) solve min = 1/2 x'*A*x with constraint (1) where B*x + 1/2 D (x o x ) = c (2) with symmetric matrix A and symmetric tensor D with a langrangian multiplier vector l we get min = 1/2 x' A x + l' ( B x + 1/2 D (x o x) ) 0 = x' A + l' B + 1/2 l' (x' D ) 0 = ( A + 1/2 l' D ) x + B' l x = - inv( A + 1/2 l o D) B' l inserting it into (2) yields 0 = - B ( inv( A + 1/2 l o D) B' l) + 1/2 D * (( inv( A + 1/2 l o D) B' l) o ( inv( A + 1/2 l o D) B' l)) - c which has to be solved for l for the starting guess (omit quadratic term with D): min = 1/2 x' A x + l' B x => x = - inv(A) B' l insert in (2) in the form "B*x = c" yields - B inv(A) B' l = c so guess l = -inv(B inv(A) B') c