1

For a Nonlinear Programming problem, what is a Kuhn Tucker Point? Is a local min. necessarily a Kuhn Tucker point?

ThinkConnect
  • 784

1 Answers1

0

A Karush-Kuhn-Tucker conditions are the necessary conditions for a critical/stationary point to be a local optimum for an inequality constrained optimization problem. Thus a Karush-Kuhn-Tucker point is a point that meets thee necessary condition for that point to be an optimum point. However, meeting these conditions is not sufficient for it to be a local optimum. A test has to be run on the Hessian of the Lagrangian function associated with the optimization problem. For a local minimum, the Hessian has to be positive-definite, and for a maximum, the Hessian has to be negative-definite. Refer to this link for more details: https://en.wikipedia.org/wiki/Positive-definite_matrix

For the Karush-Kuhn-Tucker conditions, see these refrences: https://mjo.osborne.economics.utoronto.ca/index.php/tutorial/index/1/ktc/t http://www.csc.kth.se/utbildning/kth/kurser/DD3364/Lectures/KKT.pdf

and for a good example: read the answer to "Q: Check Kuhn-Tucker conditions" in the tackExchange

Hass
  • 367
  • Note that If the Hessian has both positive and negative eigenvalues then the point is a saddle point. If all the tests fail, the point is undecidable. – Hass Feb 28 '18 at 10:50
  • "For a local minimum, the Hessian has to be positive-definite" It's not required that the hessian be positive-definite for a local minimum. The lagrangian needs to have non-negative curvature in all feasible directions, which is a weaker requirement than being positive-definite. – Ryan Burn Sep 25 '21 at 20:07