By including Davidon [7] projections in the variable metric updating we can generalise Straeter's algorithm to a family of parallel projected quasi-Newton algorithms which do not suffer the above drawbacks and
M.J.D. Powell, On the convergence of the variable metric algorithm. Mathematics Branch, Atomic Energy Research Establishment, Harwell, Berkshire, England, (October 1969) Google Scholar D.F. Shanno, Conditioning of quasi-Newton methods for function minimization. Math. Comput. 24, 647–656 (1970...
Newtonmethodify(x)=0.5xTQx-bTx,thenSk=H-1(xk)=Q(quadraticcase)ClassicalModifiedNewton抯Method:xk+1=xk-H-1(x0)y(xk)NotethattheHessianisonlyevaluatedattheinitialpoint0.x Question:WhatisameasureofeffectivenessfortheClassicalModifiedNewtonMethod?OptimizationinEngineeringDesign GeorgiaInstituteof...
• The method is also referred to as the variable metric method (originally suggested by Davidon). Quasi-Newton condition with rank two update substituted is p i = B k q i + a uu T q i + b vv T q i Set u = p k ,
We consider quasi-Newton methods for generalized equations in Banach spaces under metric regularity and give a sufficient condition for q-linear convergence. Then we show that the well-known Broyden update satisfies this sufficient condition in Hilbert spaces. We also establish various modes of q-sup...
is very similar to corrector or multiple centrality correctors in IPMs and reinforce the argument that the cost of computing a quasi-Newton step is lower than the Newton step. It is important to note that scalars\(\alpha _i\)are the same as the ones computed at step 2 of Algorithm 1. ...
In the next section we first give a modified quasi-Newton equation. In Section 3, we propose a general BFGS-type method, and study the properties of the method if some certain line search strategy is used. By using the results obtained in Section 3, we give three algorithms (Algorithm ...
Variable Metric MethodsThe major stationary iterative method used to solve nonlinear optimization problems is the quasi-Newton (QN) method. Symmetric Rank-One (SR1) is a method in the quasi-Newton family. This algorithm converges towards the true Hessian fast and has computational advantages for ...
In particular, a new robust quasi-Newton (R-QN) algorithm using the self-scaling variable metric (SSV) method for unconstrained optimization is studied in detail. Simulation results show that the R-QN algorithm is more robust to impulse noise in the desired signal than the RLS algorithm and ...
[35] to compute a quasi-periodic steady state. In this algorithm, the steady-state response is approximated with a finite number of Fourier coefficients. The arising nonlinear algebraic equations are solved either with the Picard or the Newton–Raphson iteration, where the response of the ...