• Previous Article
    A sixth order numerical method for a class of nonlinear two-point boundary value problems
  • NACO Home
  • This Issue
  • Next Article
    A smoothing Newton method for generalized Nash equilibrium problems with second-order cone constraints
2012, 2(1): 19-29. doi: 10.3934/naco.2012.2.19

Global convergence of an SQP algorithm for nonlinear optimization with overdetermined constraints

1. 

Department of Applied Mathematics, Beijing University of Technology, Beijing 100124

2. 

Department of Applied Mathematics, Hebei University of Technology, Tianjin 300401

Received  March 2011 Revised  May 2011 Published  March 2012

A sequential quadratic programming (SQP) algorithm is presented for solving nonlinear optimization with overdetermined constraints. In each iteration, the quadratic programming (QP) subproblem is always feasible even if the gradients of constraints are always linearly dependent and the overdetermined constraints may be inconsistent. The $\ell_2$ exact penalty function is selected as the merit function. Under suitable assumptions on gradients of constraints, we prove that the algorithm will terminate at an approximate KKT point of the problem, or there is a limit point which is either a point satisfying the overdetermined system of equations or a stationary point for minimizing the $\ell_2$ norm of the residual of the overdetermined system of equations.
Citation: Chunlin Hao, Xinwei Liu. Global convergence of an SQP algorithm for nonlinear optimization with overdetermined constraints. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 19-29. doi: 10.3934/naco.2012.2.19
References:
[1]

Math. Program., 111 (2008), 5-32. doi: doi:10.1007/s10107-006-0077-1.  Google Scholar

[2]

Comput. Optim. Appl., 28 (2004), 51-86. doi: doi:10.1023/B:COAP.0000018879.40214.11.  Google Scholar

[3]

J. Comput. Appl. Math., 120 (2000), 27-40. doi: doi:10.1016/S0377-0427(00)00301-0.  Google Scholar

[4]

J. Math. Anal. Appl., 139 (1989), 319-351. doi: doi:10.1016/0022-247X(89)90111-X.  Google Scholar

[5]

Math. Program., 43 (1989), 277-303. doi: doi:10.1007/BF01582294.  Google Scholar

[6]

SIAM J. Optim., 19 (2008), 351-369. doi: doi:10.1137/060674004.  Google Scholar

[7]

Math. Program., 99 (2004), 127-148. doi: doi:10.1007/s10107-003-0376-8.  Google Scholar

[8]

SIAM, Philadelphia, USA, 2000. doi: doi:10.1137/1.9780898719857.  Google Scholar

[9]

Science Press, 2001. Google Scholar

[10]

John Wiley and Sons, Chichester, UK, 1981.  Google Scholar

[11]

SIAM J. Optim., 13 (2002), 635-659. doi: doi:10.1137/S1052623499357258.  Google Scholar

[12]

Math. Program., 91 (2002), 239-269. doi: doi:10.1007/s101070100244.  Google Scholar

[13]

Third Edition, The Johns Hopkins University Press, 1996.  Google Scholar

[14]

J. Optim. Theory Appl., 22 (1977), 297-309. doi: doi:10.1007/BF00932858.  Google Scholar

[15]

SIAM J. Optim., 12 (2002), 283-302. doi: doi:10.1137/S1052623499361543.  Google Scholar

[16]

J. Comput. Appl. Math., 180 (2005), 201-211. doi: doi:10.1016/j.cam.2004.10.012.  Google Scholar

[17]

SIAM J. Optim., 14 (2004), 1163-1186. doi: doi:10.1137/S1052623402400641.  Google Scholar

[18]

Math. Program., 125 (2010), 163-193. doi: doi:10.1007/s10107-009-0272-y.  Google Scholar

[19]

SIAM J. Optim., 21 (2011), 545-571. doi: 10.1137/080739884.  Google Scholar

[20]

J. Comput. Optim. Appl., 7 (1997), 127-142. doi: doi:10.1023/A:1008671829454.  Google Scholar

[21]

Springer-Verlag New York, Inc., 1999. doi: doi:10.1007/b98874.  Google Scholar

[22]

in "Proceedings 1977 Dundee Biennial Conference on Numerical Analysis"(ed. G.A. Watson), Springer-Verlag, Berlin, 1978, 144-157.  Google Scholar

[23]

Math. Program., 82 (1998), 413-448. doi: doi:10.1007/BF01580078.  Google Scholar

[24]

Lecture Notes in "Computer Science, Global Optimization and Constraint Satisfaction"(eds. C. Blieket al.), COCOS 2002, LNCS 2861, 171-177, Springer Berlin Heidelberg, 2003. Google Scholar

[25]

SIAM J. Optim., 13 (2002), 470-497. doi: doi:10.1137/S1052623498333731.  Google Scholar

[26]

Numer. Math., 70 (1995), 515-539. doi: doi:10.1007/s002110050133.  Google Scholar

show all references

References:
[1]

Math. Program., 111 (2008), 5-32. doi: doi:10.1007/s10107-006-0077-1.  Google Scholar

[2]

Comput. Optim. Appl., 28 (2004), 51-86. doi: doi:10.1023/B:COAP.0000018879.40214.11.  Google Scholar

[3]

J. Comput. Appl. Math., 120 (2000), 27-40. doi: doi:10.1016/S0377-0427(00)00301-0.  Google Scholar

[4]

J. Math. Anal. Appl., 139 (1989), 319-351. doi: doi:10.1016/0022-247X(89)90111-X.  Google Scholar

[5]

Math. Program., 43 (1989), 277-303. doi: doi:10.1007/BF01582294.  Google Scholar

[6]

SIAM J. Optim., 19 (2008), 351-369. doi: doi:10.1137/060674004.  Google Scholar

[7]

Math. Program., 99 (2004), 127-148. doi: doi:10.1007/s10107-003-0376-8.  Google Scholar

[8]

SIAM, Philadelphia, USA, 2000. doi: doi:10.1137/1.9780898719857.  Google Scholar

[9]

Science Press, 2001. Google Scholar

[10]

John Wiley and Sons, Chichester, UK, 1981.  Google Scholar

[11]

SIAM J. Optim., 13 (2002), 635-659. doi: doi:10.1137/S1052623499357258.  Google Scholar

[12]

Math. Program., 91 (2002), 239-269. doi: doi:10.1007/s101070100244.  Google Scholar

[13]

Third Edition, The Johns Hopkins University Press, 1996.  Google Scholar

[14]

J. Optim. Theory Appl., 22 (1977), 297-309. doi: doi:10.1007/BF00932858.  Google Scholar

[15]

SIAM J. Optim., 12 (2002), 283-302. doi: doi:10.1137/S1052623499361543.  Google Scholar

[16]

J. Comput. Appl. Math., 180 (2005), 201-211. doi: doi:10.1016/j.cam.2004.10.012.  Google Scholar

[17]

SIAM J. Optim., 14 (2004), 1163-1186. doi: doi:10.1137/S1052623402400641.  Google Scholar

[18]

Math. Program., 125 (2010), 163-193. doi: doi:10.1007/s10107-009-0272-y.  Google Scholar

[19]

SIAM J. Optim., 21 (2011), 545-571. doi: 10.1137/080739884.  Google Scholar

[20]

J. Comput. Optim. Appl., 7 (1997), 127-142. doi: doi:10.1023/A:1008671829454.  Google Scholar

[21]

Springer-Verlag New York, Inc., 1999. doi: doi:10.1007/b98874.  Google Scholar

[22]

in "Proceedings 1977 Dundee Biennial Conference on Numerical Analysis"(ed. G.A. Watson), Springer-Verlag, Berlin, 1978, 144-157.  Google Scholar

[23]

Math. Program., 82 (1998), 413-448. doi: doi:10.1007/BF01580078.  Google Scholar

[24]

Lecture Notes in "Computer Science, Global Optimization and Constraint Satisfaction"(eds. C. Blieket al.), COCOS 2002, LNCS 2861, 171-177, Springer Berlin Heidelberg, 2003. Google Scholar

[25]

SIAM J. Optim., 13 (2002), 470-497. doi: doi:10.1137/S1052623498333731.  Google Scholar

[26]

Numer. Math., 70 (1995), 515-539. doi: doi:10.1007/s002110050133.  Google Scholar

[1]

Amira Khelifa, Yacine Halim. Global behavior of P-dimensional difference equations system. Electronic Research Archive, , () : -. doi: 10.3934/era.2021029

[2]

Qing Liu, Bingo Wing-Kuen Ling, Qingyun Dai, Qing Miao, Caixia Liu. Optimal maximally decimated M-channel mirrored paraunitary linear phase FIR filter bank design via norm relaxed sequential quadratic programming. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1993-2011. doi: 10.3934/jimo.2020055

[3]

Flank D. M. Bezerra, Jacson Simsen, Mariza Stefanello Simsen. Convergence of quasilinear parabolic equations to semilinear equations. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3823-3834. doi: 10.3934/dcdsb.2020258

[4]

Giulio Ciraolo, Antonio Greco. An overdetermined problem associated to the Finsler Laplacian. Communications on Pure & Applied Analysis, 2021, 20 (3) : 1025-1038. doi: 10.3934/cpaa.2021004

[5]

Manoel J. Dos Santos, Baowei Feng, Dilberto S. Almeida Júnior, Mauro L. Santos. Global and exponential attractors for a nonlinear porous elastic system with delay term. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2805-2828. doi: 10.3934/dcdsb.2020206

[6]

Jiangxing Wang. Convergence analysis of an accurate and efficient method for nonlinear Maxwell's equations. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2429-2440. doi: 10.3934/dcdsb.2020185

[7]

Bernold Fiedler, Carlos Rocha, Matthias Wolfrum. Sturm global attractors for $S^1$-equivariant parabolic equations. Networks & Heterogeneous Media, 2012, 7 (4) : 617-659. doi: 10.3934/nhm.2012.7.617

[8]

Nizami A. Gasilov. Solving a system of linear differential equations with interval coefficients. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2739-2747. doi: 10.3934/dcdsb.2020203

[9]

Ying Yang. Global classical solutions to two-dimensional chemotaxis-shallow water system. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2625-2643. doi: 10.3934/dcdsb.2020198

[10]

Jinyi Sun, Zunwei Fu, Yue Yin, Minghua Yang. Global existence and Gevrey regularity to the Navier-Stokes-Nernst-Planck-Poisson system in critical Besov-Morrey spaces. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3409-3425. doi: 10.3934/dcdsb.2020237

[11]

Harumi Hattori, Aesha Lagha. Global existence and decay rates of the solutions for a chemotaxis system with Lotka-Volterra type model for chemoattractant and repellent. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021071

[12]

Bin Pei, Yong Xu, Yuzhen Bai. Convergence of p-th mean in an averaging principle for stochastic partial differential equations driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 1141-1158. doi: 10.3934/dcdsb.2019213

[13]

Cheng Wang. Convergence analysis of Fourier pseudo-spectral schemes for three-dimensional incompressible Navier-Stokes equations. Electronic Research Archive, , () : -. doi: 10.3934/era.2021019

[14]

Nouressadat Touafek, Durhasan Turgut Tollu, Youssouf Akrour. On a general homogeneous three-dimensional system of difference equations. Electronic Research Archive, , () : -. doi: 10.3934/era.2021017

[15]

Yingdan Ji, Wen Tan. Global well-posedness of a 3D Stokes-Magneto equations with fractional magnetic diffusion. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3271-3278. doi: 10.3934/dcdsb.2020227

[16]

Brahim Alouini. Finite dimensional global attractor for a class of two-coupled nonlinear fractional Schrödinger equations. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021013

[17]

Yongqiang Fu, Xiaoju Zhang. Global existence and asymptotic behavior of weak solutions for time-space fractional Kirchhoff-type diffusion equations. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021091

[18]

Xin Zhong. Global strong solution and exponential decay for nonhomogeneous Navier-Stokes and magnetohydrodynamic equations. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3563-3578. doi: 10.3934/dcdsb.2020246

[19]

Xuemin Deng, Yuelong Xiao, Aibin Zang. Global well-posedness of the $ n $-dimensional hyper-dissipative Boussinesq system without thermal diffusivity. Communications on Pure & Applied Analysis, 2021, 20 (3) : 1229-1240. doi: 10.3934/cpaa.2021018

[20]

Najeeb Abdulaleem. $ V $-$ E $-invexity in $ E $-differentiable multiobjective programming. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021014

 Impact Factor: 

Metrics

  • PDF downloads (48)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]