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Iteration Complexity of an Inner Accelerated Inexact Proximal Augmented Lagrangian Method Based on the Classical Lagrangian Function

This paper establishes the iteration complexity of an inner accelerated inexact proximal augmented Lagrangian (IAIPAL) method for solving linearly constrained smooth nonconvex composite optimization problems that is based on the classical augmented Lagrangian (AL) function. More specifically, each IAIPAL iteration consists of inexactly solving a proximal AL subproblem by an accelerated composite gradient (ACG) method followed by a classical Lagrange multiplier update. Under the assumption that the domain of the composite function is bounded and the problem has a Slater point, it is shown that IAIPAL generates an approximate stationary solution in
ACG iterations where is a tolerance for both stationarity and feasibility. Moreover, the above bound is derived without assuming that the initial point is feasible. Finally, numerical results are presented to demonstrate the strong practical performance of IAIPAL.

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON OPTIMIZATION; Vol.33 No.1 January-March 2023

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 181-210

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

ITERATION COMPLEXITY
INEXACT PROXIMAL AUGMENTED LAGRANGIAN METHOD
INNER ACCELERATED FIRST-ORDER METHODS

Info Detail Spesifik

https://doi.org/10.1137/20M136147X

Pernyataan Tanggungjawab

Weiwei Kong, Jefferson G. Melo, Renato D. C. Monteiro

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