Search results
Results from the WOW.Com Content Network
If the Cauchy point is inside the trust region, the new solution is taken at the intersection between the trust region boundary and the line joining the Cauchy point and the Gauss-Newton step (dog leg step). [2] The name of the method derives from the resemblance between the construction of the dog leg step and the shape of a dogleg hole in ...
In mathematical optimization, a trust region is the subset of the region of the objective function that is approximated using a model function (often a quadratic).If an adequate model of the objective function is found within the trust region, then the region is expanded; conversely, if the approximation is poor, then the region is contracted.
LMA can also be viewed as Gauss–Newton using a trust region approach. The algorithm was first published in 1944 by Kenneth Levenberg , [ 1 ] while working at the Frankford Army Arsenal . It was rediscovered in 1963 by Donald Marquardt , [ 2 ] who worked as a statistician at DuPont , and independently by Girard, [ 3 ] Wynne [ 4 ] and Morrison.
Powell's method, strictly Powell's conjugate direction method, is an algorithm proposed by Michael J. D. Powell for finding a local minimum of a function. The function need not be differentiable, and no derivatives are taken. The function must be a real-valued function of a fixed number of real-valued inputs.
It addressed the instability issue of another algorithm, the Deep Q-Network (DQN), by using the trust region method to limit the KL divergence between the old and new policies. However, TRPO uses the Hessian matrix (a matrix of second derivatives) to enforce the trust region, but the Hessian is inefficient for large-scale problems.
Newton's method is a special case of a curve-fitting method, in which the curve is a degree-two polynomial, constructed using the first and second derivatives of f. If the method is started close enough to a non-degenerate local minimum (= with a positive second derivative), then it has quadratic convergence .
The first and still popular method for ensuring convergence relies on line searches, which optimize a function along one dimension. A second and increasingly popular method for ensuring convergence uses trust regions. Both line searches and trust regions are used in modern methods of non-differentiable optimization.
It was the first quasi-Newton method to generalize the secant method to a multidimensional problem. This update maintains the symmetry and positive definiteness of the Hessian matrix . Given a function f ( x ) {\displaystyle f(x)} , its gradient ( ∇ f {\displaystyle \nabla f} ), and positive-definite Hessian matrix B {\displaystyle B} , the ...