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• Sequential quadratic programming
  ==Hessian matrix update== ... programming. The most popular and useful method to generate an approximate Hessian matrix is [[BFGS method]].
  6 KB (930 words) - 00:10, 26 October 2007
• Optimality conditions (NLP)
  ... </math>, which can be tested by checking that all [[eigenvalues]] of the [[Hessian]] matrix at the candidate point are positive. ... efinite]] on the subspace tangent to the [[active constraints]]. Because a Hessian matrix is symmetric, it is positive definite when all eigenvalues are posi ...
  6 KB (904 words) - 20:16, 22 September 2008
• Nash equilibrium
  ... {s_0} </math> is a minimum (and thus not a Nash Equilibrium point). If the Hessian is equal to 0 at <math> \mathbf{s_0} </math>, we cannot draw any informati ...
  6 KB (841 words) - 14:56, 9 May 2008
• Lagrange multipliers
  ... ction of n+k variables. If the gradient of the Langrangian is zero and the Hessian of the Lagrangian is positive definite, then we have found a locally const ...
  2 KB (314 words) - 18:08, 11 January 2007
• SNOPT
  ... ctive function and constraints. It uses quasi-Newton approximations to the Hessian of the augmented Lagrangian function to finding search direction toward op ...
  1 KB (154 words) - 19:03, 18 March 2007
• BFGS method
  ... to generate approximate Hessian matrix. Avoiding the calculation of exact Hessian (2nd-order gradient) can save significant computational cost during iterat ... where '''B''' is the approximate Hessian matrix used in iteration
  2 KB (227 words) - 17:47, 23 September 2007
• Introduction to random utility discrete choice models
  ... it equal to zero, solve the resulting system of equations, and check the [[Hessian]] for sufficiency. Alternatively, we can use a numerical [[optimization]] ...
  34 KB (5423 words) - 01:24, 15 March 2010
• Taylor series
  ... = \mathbf{x}_0</math> and <math>\nabla^2 f(\mathbf{x}_0)\!</math> is the [[Hessian]] of <math>\,f</math> evaluated at <math>\mathbf{x} = \mathbf{x}_0</math>.
  1 KB (232 words) - 20:44, 20 January 2010

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