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Quadratic Convergence of Smoothing Newton's Method for 0/1 Loss Optimization

It has been widely recognized that the 0/1-loss function is one of the most natural choices for modelling classification errors, and it has a wide range of applications including support vector machines and 1-bit compressed sensing. Due to the combinatorial nature of the 0/1 loss function, methods based on convex relaxations or smoothing approximations have dominated the existing research and are often able to provide approximate solutions of good quality. However, those methods are not optimizing the 0/1 loss function directly and hence no optimality has been established for the original problem. This paper aims to study the optimality conditions of the 0/1 function minimization and for the first time to develop Newton's method that directly optimizes the 0/1 function with a local quadratic convergence under reasonable conditions. Extensive numerical experiments demonstrate its superior performance as one would expect from Newton-type methods.

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON OPTIMIZATION; Vol.31 No.4 October-December 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 3184-3211

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

OPTIMALITY CONDITIONS
NEWTON'S METHOD
0/1 LOSS FUNCTION
LOCALLY QUADRATIC CONVERGENCE
SUPERIOR NUMERICAL PERFORMANCE

Info Detail Spesifik

https://doi.org/10.1137/21M1409445

Pernyataan Tanggungjawab

Shenglong Zhou, Lili Pan, Naihua Xiu, Hou-Duo Qi

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