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Displaying similar documents to “A generalized limited-memory BNS method based on the block BFGS update”

Application of the infinitely many times repeated BNS update and conjugate directions to limited-memory optimization methods

Vlček, Jan, Lukšan, Ladislav

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To improve the performance of the L-BFGS method for large scale unconstrained optimization, repeating of some BFGS updates was proposed e.g. in [1]. Since this can be time consuming, the extra updates need to be selected carefully. We show that groups of these updates can be repeated infinitely many times under some conditions, without a noticeable increase of the computational time; the limit update is a block BFGS update [17]. It can be obtained by solving of some Lyapunov matrix equation...

A modified limited-memory BNS method for unconstrained minimization derived from the conjugate directions idea

Vlček, Jan, Lukšan, Ladislav

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A modification of the limited-memory variable metric BNS method for large scale unconstrained optimization of the differentiable function f : ℛ N → ℛ is considered, which consists in corrections (based on the idea of conjugate directions) of difference vectors for better satisfaction of the previous quasi-Newton conditions. In comparison with [11], more previous iterations can be utilized here. For quadratic objective functions, the improvement of convergence is the best one in some sense, all...

Modifications of the limited-memory BFGS method based on the idea of conjugate directions

Vlček, Jan, Lukšan, Ladislav

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Simple modifications of the limited-memory BFGS method (L-BFGS) for large scale unconstrained optimization are considered, which consist in corrections of the used difference vectors (derived from the idea of conjugate directions), utilizing information from the preceding iteration. For quadratic objective functions, the improvement of convergence is the best one in some sense and all stored difference vectors are conjugate for unit stepsizes. The algorithm is globally convergent for...

An improved nonmonotone adaptive trust region method

Yanqin Xue, Hongwei Liu, Zexian Liu (2019)

Applications of Mathematics

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Trust region methods are a class of effective iterative schemes in numerical optimization. In this paper, a new improved nonmonotone adaptive trust region method for solving unconstrained optimization problems is proposed. We construct an approximate model where the approximation to Hessian matrix is updated by the scaled memoryless BFGS update formula, and incorporate a nonmonotone technique with the new proposed adaptive trust region radius. The new ratio to adjusting the next trust...