Note sur la convergence de méthodes de directions conjuguées

By Série Rouge, E. Polak, G. Ribière. 1969

Subfields: Mathematical Optimization, Numerical Methods & Scientific Computing

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Citations in the corpus

Numerical optimization (2004, methodology): “The Polak–Ribière method was introduced in [237], and the example showing that it may fail to converge on nonconvex problems is given by Powell [253].”
A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search (2005, unknown): “Similar to the approach [13, 20, 38] taken for the Polak–Ribière– Polyak [31, 32] version of the conjugate gradient method, we establish convergence for general nonlinear functions by restricting the lower value of β k .”
Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich-Schwoebel Type Energy: Application to Thin Film Epitaxy (2012, methodology): “To compute the results given in section 6 we use the simple Polak–Ribiére variant of the nonlinear conjugate gradient method for the minimization step [23].”
Deformable Medical Image Registration: A Survey (2013, methodology): “Among the well-known formulas for βt, one may cite the Fletcher-Reeves [404], the Polak-Ribière [405], the Polak-RibièrePolyak [406] and the Hestenes-Stiefel [407].”
A descent modified Polak–Ribière–Polyak conjugate gradient method and its global convergence (2006, methodology): “The global convergence of the PRP method with exact line search has been proved in Polak & Ribiere (1969) under strong convexity assumption on f .”
Convergence Properties of the BFGS Algoritm (2002, methodology): “However, the following questions have remained open for many years (for example, see Nocedal [9] and Yuan [21]): (i) does the DFP method with Wolfe line searches converge for convex functions? and (ii) does the BFGS method with Wolfe line searches converge for nonconvex functions? In this paper, we ”
Unconditionally stable schemes for equations of thin film epitaxy (2010, methodology): “To solve the resulting nonlinear finite-difference equations at the implicit time level, we employ a nonlinear conjugate gradient method, using the Polak Ribiére formula [18] to determine the line search direction.”