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...
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 ...
,Self-Scaling Variable Metric Algorithm Without Line-Search for Unconstrained Minimization, Mathematics of Computation, Vol. 27, pp. 873–885, 1973. Google Scholar Greenstadt, J.,Variations on Variable Metric Methods, Mathematics of Computation, Vol. 24, pp. 1–22, 1970. Google Scholar ...
• 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 ,
Davidon WC (1959) Variable metric method for minimization. Technical report, Argonne National Lab. https://www.osti.gov/biblio/4252678 Deaton JD, Grandhi RV (2014) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidisc Optim 49(1):1–38. https...
Another class of methods that do not require explicit expressions for the second derivatives is the class of quasi-Newton methods . These are sometimes referred to as variable metric methods . DOI: 10.1007/0-387-24149-3_7 年份: 2018
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 ...
We show that on complete doubling metric measure spaces X supporting a Poincare inequality, all Newton-Sobolev functions u are quasicontinuous, i.e. that for every epsilon > 0 there is an open set U subset of X such that C-p(U) < epsilon and the restriction of u to X\U is continuou...
(10). In the Registration Refinement Block, it is used to improve convergence of the self-supervised algorithm, based on minimising the photometric error in Eq. (12). We investigate the effect of this term in both depth and registration accuracy, when testing with real data. We show in ...
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 ...