English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper, an efficient modified Newton type algorithm is proposed fornonlinear unconstrianed optimization problems. The modified Hessian is a convexcombination of the identity matrix (for steepest descent algorithm) and theHessian matrix (for Newton algorithm). The coefficients of the convexcombination are dynamically chosen in every iteration. The algorithm is provedto be globally and quadratically convergent for (convex and nonconvex)nonlinear functions. Efficient implementation is described. Numerical test onwidely used CUTE test problems is conducted for the new algorithm. The testresults are compared with those obtained by MATLAB optimization toolboxfunction {\tt fminunc}. The test results are also compared with those obtainedby some established and state-of-the-art algorithms, such as a limited memoryBFGS, a descent and conjugate gradient algorithm, and a limited memory anddescent conjugate gradient algorithm. The comparisons show that the newalgorithm is promising.

A Globally and Quadratically Convergent Algorithm with Efficient Implementation for Unconstrained Optimization