NewtonsMethod:

Path: Math/Analysis

% Solve an optimization problem with Newton's method. 
 Requires the objective value, gradient vector, and hessian matrix to be
 defined with function handles.
   
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   Form:
   [xopt,nSteps,cpuTime,iterate,objValue] = ...
     NewtonsMethod(f,grad,hess,x,stopData,stepSizeData);

   See also:  Armijo.m, NLEqSolver.m
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   ------
   Inputs
   ------
   f             @(x)   Function handle for cost function
   grad          @(x)   Function handle for gradient of cost function
   hess          @(x)   Function handle for hessian of cost function
   x             (n,1)  Initial state
   stopData      .      Data structure with fields:
                 .fun     Function handle with arguments "f(x), grad(x)"
                          returning true if stop conditions met, else false.
                 .maxIter Maximum number of iterations.
                 .gTol    Gradient norm tolerance. Stop when norm of gradient
                          vector is below this threshold.
   stepSizeData  .rule    Name of the stepsize rule. 3 choices:
                             - Constant  (define s)
                             - Armijo    (define s, sigma, beta)
                 .s       Scalar stepsize.
                 .sigma   Scale factor for Armijo rule
                 .beta    Scale factor for Armijo rule

   -------
   Outputs
   -------
   xopt          (n,1)       Optimal solution
   nSteps        (1,1)       Number of iteration steps computed
   cpuTime       (1,1)       Total time to execute, in seconds
   iterate       (1,nSteps)  History of iterate
   objValue      (1,nSteps)  History of objective value

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Children:

Math: Analysis/Armijo

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