JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (4): 102-107.doi: 10.6040/j.issn.1671-9352.0.2019.815

Previous Articles    

Optimizing the efficiency of first-order methods for the distance to an optimal solution of smooth convex functions

CHEN Qian-zhu, HU Hai-ping*   

  1. School of Science, Shanghai University, Shanghai 200444, China
  • Published:2020-04-09

PDF (PC)

377

Abstract: We use the performance estimation problem(PEP)method to optimize the step coefficient of the first-order smooth convex minimization method by studying the worst-case estimation of the optimal solution distance ‖xN-x*‖2, and the convergence rate can reach O(1/N 2).

Key words: first-order method, smooth convex minimization, worst-case performance analysis, rate of convergence

CLC Number: 

  • O224
[1] NESTEROV Y. A method for unconstrained convex minimization problem with the rate of convergence O(1/k2)[J]. Soviet Mathematics Doklady, 1983, 27:372-376.
[2] NESTEROV Y. Smooth minimization of non-smooth functions[J]. Math Program, 2005, 103(1):127-152.
[3] DRORI Y,TEBOULLE M. Performance of first-order methods for smooth convex minimization: a novel approach[J]. Mathematical Programming, 2014, 145(1/2):451-482.
[4] KIM D, FESSLER J A. Optimized first-order methods for smooth convex minimization[J]. Mathematical Programming, 2016, 159(1/2):81-107.
[5] TAYLOR A B, HENDRICKX J M, GLINEUR F. Smooth strongly convex interpolation and exact worst-case performance of first-order methods[J]. Mathematical Programming, 2017, 161(1): 307-345.
[6] NEMIROVSKY A. Information-based complexity of linear operator equations[J]. Journal of Complexity, 1992, 8(2):153-175.
[1] HUANG Ai-ling, LIN Shuai. Finite dimensional approximation of linear stochastic Schrödinger equation in terms of localization of quantum Bernoulli noises [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 67-71.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd