线性约束两分块非凸优化的ADMM-SQP算法
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Abstract Based on the alternating direction method of multipliers (ADMM) and the sequential quadratic programming (SQP) method, this paper proposes a new efficient algorithm for two blocks nonconvex optimization with linear constrained. Firstly, taking SQP thought as the main line, the quadratic programming (QP) is decomposed into two independent small scale QP according to ADMM idea. Secondly, the new iteration point of the prime variable is generated by Armijo line search for the augmented Lagrange function. Finally, the dual variables are updated by an explicit expression. Thus, a new ADMM-SQP algorithm is constructed. Under the weaker conditions, the global convergence of the algorithm is analyzed. Some preliminary numerical results are reported to support the efficiency of the new algorithm.
Chinese Library Classification O221
ÂvFϵ2017-11-08 *Ä7‘8: I[g,‰ÆÄ7(Nos. 11771383, 11601095), 2Üg,‰ÆÄ7(Nos. 2016GXNSFDA 380019, 2016GXNSFBA380185) 1. 2ÜŒÆêƆ&E‰ÆÆ , Hw 530004; College of Mathematics and Information Science, Guangxi University, Nanning 530004, China 2. 2ܬxŒÆnÆ , Hw 530007; College of Science, Guangxi University of Nationalities, Nanning 530007, China 3. Œ “‰Æ êƆÚOÆ , 2Üp E,XÚ`z†Œêâ-:¢ ¿, 2ÜŒ 537000; School of Mathematics and Statistics, Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, Guangxi, China † Ï&Šö E-mail: jianjb@gxu.edu.cn
'…c ‚5 å, ü©¬šà`z, ¦f O••{, S g5y, Ž{ ¥ã©aÒ O221 2010 êÆ©aÒ 0C30, 65K05
ADMM-SQP algorithm for wk.baidu.comwo blocks linear constrained nonconvex optimization∗
JIAN Jinbao1,2,† LAO Yixian1 CHAO Miantao1 MA Guodong3
Keywords linear constrained, two blocks nonconvex optimization, alternating direction method of multipliers, sequential quadratic programming method, algorithm
2018c6 June, 2018
$ÊÆÆ Operations Research Transactions
DOI: 10.15960/j.cnki.issn.1007-6093.2018.02.007
122ò 12Ï Vol.22 No.2
‚5 åü©¬šà`z ADMM-SQP Ž{∗
{7 1,2,† NÈj1 x›71 êIÅ3
80
{7 , NÈj, x›7, êIÅ
22ò
2010 Mathematics Subject Classification 90C30
0 Úó
•Ä‚5 åü©¬`z¯Kµ
min f (x) + θ(y) s.t. Ax + By = b,
x ∈ X, y ∈ Y,
(0.1)
Ù¥f : Rn1 → R, θ : Rn2 → R, A ∈ Rm×n1 , B ∈ Rm×n2 , X ÚY©O•Rn1 ÚRn2 ¥ 4 à8. /X¯K(0.1) `z¯K3&ÒÚã”?n!êâ ÷!DÕ`z +•¥kX ›©2• A^. du¯K(0.1) 8I¼êäkŒ©( , &ÄÙAÏk ¦)gŽ Ú•{, äk-‡ ‰Æ¿ÂÚA^dŠ. ˜«å»´: <‚ÄuDouglas-Rachford© Ž {gŽ[1,2], /ÏuŒ©`z éó¯K[3,4], ïÚØy Œ©`z¯õ ¦f O•• {(ADMM), Ü©©z„ [5-12].
Á‡ Äu¦f O••{(ADMM)ÚS g5y(SQP)•{gŽ, —åuïÄ‚5 åü©¬šà`z #.p Ž{. Äk, ±SQPgŽ•Ì‚, 3Ù g5y(QP)f¯K ¦)¥Ú\ADMMgŽ, òQP©)•ü‡ƒpÕá 5 QP¦). Ùg, /ÏO2. ‚KF¼êÚArmijo‚|¢ ) ©Cþ#S“:. • , ±wª)Ûª•#éóCþ. Ï d, ï ˜‡#.ADMM-SQPŽ{. 3 f^‡e, ©Û Ž{Ï~¿Âe ÛÂñ 5, ¿éŽ{?1 ÐÚ êŠÁ .
Chinese Library Classification O221
ÂvFϵ2017-11-08 *Ä7‘8: I[g,‰ÆÄ7(Nos. 11771383, 11601095), 2Üg,‰ÆÄ7(Nos. 2016GXNSFDA 380019, 2016GXNSFBA380185) 1. 2ÜŒÆêƆ&E‰ÆÆ , Hw 530004; College of Mathematics and Information Science, Guangxi University, Nanning 530004, China 2. 2ܬxŒÆnÆ , Hw 530007; College of Science, Guangxi University of Nationalities, Nanning 530007, China 3. Œ “‰Æ êƆÚOÆ , 2Üp E,XÚ`z†Œêâ-:¢ ¿, 2ÜŒ 537000; School of Mathematics and Statistics, Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, Guangxi, China † Ï&Šö E-mail: jianjb@gxu.edu.cn
'…c ‚5 å, ü©¬šà`z, ¦f O••{, S g5y, Ž{ ¥ã©aÒ O221 2010 êÆ©aÒ 0C30, 65K05
ADMM-SQP algorithm for wk.baidu.comwo blocks linear constrained nonconvex optimization∗
JIAN Jinbao1,2,† LAO Yixian1 CHAO Miantao1 MA Guodong3
Keywords linear constrained, two blocks nonconvex optimization, alternating direction method of multipliers, sequential quadratic programming method, algorithm
2018c6 June, 2018
$ÊÆÆ Operations Research Transactions
DOI: 10.15960/j.cnki.issn.1007-6093.2018.02.007
122ò 12Ï Vol.22 No.2
‚5 åü©¬šà`z ADMM-SQP Ž{∗
{7 1,2,† NÈj1 x›71 êIÅ3
80
{7 , NÈj, x›7, êIÅ
22ò
2010 Mathematics Subject Classification 90C30
0 Úó
•Ä‚5 åü©¬`z¯Kµ
min f (x) + θ(y) s.t. Ax + By = b,
x ∈ X, y ∈ Y,
(0.1)
Ù¥f : Rn1 → R, θ : Rn2 → R, A ∈ Rm×n1 , B ∈ Rm×n2 , X ÚY©O•Rn1 ÚRn2 ¥ 4 à8. /X¯K(0.1) `z¯K3&ÒÚã”?n!êâ ÷!DÕ`z +•¥kX ›©2• A^. du¯K(0.1) 8I¼êäkŒ©( , &ÄÙAÏk ¦)gŽ Ú•{, äk-‡ ‰Æ¿ÂÚA^dŠ. ˜«å»´: <‚ÄuDouglas-Rachford© Ž {gŽ[1,2], /ÏuŒ©`z éó¯K[3,4], ïÚØy Œ©`z¯õ ¦f O•• {(ADMM), Ü©©z„ [5-12].
Á‡ Äu¦f O••{(ADMM)ÚS g5y(SQP)•{gŽ, —åuïÄ‚5 åü©¬šà`z #.p Ž{. Äk, ±SQPgŽ•Ì‚, 3Ù g5y(QP)f¯K ¦)¥Ú\ADMMgŽ, òQP©)•ü‡ƒpÕá 5 QP¦). Ùg, /ÏO2. ‚KF¼êÚArmijo‚|¢ ) ©Cþ#S“:. • , ±wª)Ûª•#éóCþ. Ï d, ï ˜‡#.ADMM-SQPŽ{. 3 f^‡e, ©Û Ž{Ï~¿Âe ÛÂñ 5, ¿éŽ{?1 ÐÚ êŠÁ .