American Institute of Mathematical Sciences

Advanced
2003, 2003(Special): 30-41. doi: 10.3934/proc.2003.2003.30

Constrained envelope for a general class of design problems

Ernesto Aranda 1, and  Pablo Pedregal 2,

1. 

E.T.S. Ingenieros Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
2. 

E.T.S. Ingenieros Industriales, Universidad de Castilla La Mancha

Received  July 2002 Published  April 2003

We analyze the relaxation and computation of the relaxed density when we reformulate a typical optimal design problem with volume constraint in two dimension as a fully vector variational problem. Our aim is to examine a general cost functional depending explicitly on all variables and in particular in the gradient variable, and see how far computations and properties of the relaxed integrand can be pushed.
Keywords: constrained quasiconvexification., relaxation, Optimal design.
Mathematics Subject Classification: 49J45, 74P1.
Citation: Ernesto Aranda, Pablo Pedregal. Constrained envelope for a general class of design problems. Conference Publications, 2003, 2003 (Special) : 30-41. doi: 10.3934/proc.2003.2003.30
[1]

Pablo Pedregal. Fully explicit quasiconvexification of the mean-square deviation of the gradient of the state in optimal design. Electronic Research Announcements, 2001, 7: 72-78.

[2]

Bin Li, Kok Lay Teo, Cheng-Chew Lim, Guang Ren Duan. An optimal PID controller design for nonlinear constrained optimal control problems. Discrete & Continuous Dynamical Systems - B, 2011, 16 (4) : 1101-1117. doi: 10.3934/dcdsb.2011.16.1101
[3]

Ciro D'Apice, Peter I. Kogut, Rosanna Manzo. On relaxation of state constrained optimal control problem for a PDE-ODE model of supply chains. Networks & Heterogeneous Media, 2014, 9 (3) : 501-518. doi: 10.3934/nhm.2014.9.501
[4]

José C. Bellido, Pablo Pedregal. Explicit quasiconvexification for some cost functionals depending on derivatives of the state in optimal designing. Discrete & Continuous Dynamical Systems - A, 2002, 8 (4) : 967-982. doi: 10.3934/dcds.2002.8.967
[5]

Helene Frankowska, Elsa M. Marchini, Marco Mazzola. A relaxation result for state constrained inclusions in infinite dimension. Mathematical Control & Related Fields, 2016, 6 (1) : 113-141. doi: 10.3934/mcrf.2016.6.113
[6]

Yong Xia, Yu-Jun Gong, Sheng-Nan Han. A new semidefinite relaxation for $L_{1}$-constrained quadratic optimization and extensions. Numerical Algebra, Control & Optimization, 2015, 5 (2) : 185-195. doi: 10.3934/naco.2015.5.185
[7]

Amir Adibzadeh, Mohsen Zamani, Amir A. Suratgar, Mohammad B. Menhaj. Constrained optimal consensus in dynamical networks. Numerical Algebra, Control & Optimization, 2019, 9 (3) : 349-360. doi: 10.3934/naco.2019023
[8]

H. T. Banks, R. A. Everett, Neha Murad, R. D. White, J. E. Banks, Bodil N. Cass, Jay A. Rosenheim. Optimal design for dynamical modeling of pest populations. Mathematical Biosciences & Engineering, 2018, 15 (4) : 993-1010. doi: 10.3934/mbe.2018044
[9]

K.F.C. Yiu, K.L. Mak, K. L. Teo. Airfoil design via optimal control theory. Journal of Industrial & Management Optimization, 2005, 1 (1) : 133-148. doi: 10.3934/jimo.2005.1.133
[10]

Boris P. Belinskiy. Optimal design of an optical length of a rod with the given mass. Conference Publications, 2007, 2007 (Special) : 85-91. doi: 10.3934/proc.2007.2007.85
[11]

Yannick Privat, Emmanuel Trélat. Optimal design of sensors for a damped wave equation. Conference Publications, 2015, 2015 (special) : 936-944. doi: 10.3934/proc.2015.0936
[12]

Wei Xu, Liying Yu, Gui-Hua Lin, Zhi Guo Feng. Optimal switching signal design with a cost on switching action. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-19. doi: 10.3934/jimo.2019068
[13]

Xueling Zhou, Bingo Wing-Kuen Ling, Hai Huyen Dam, Kok-Lay Teo. Optimal design of window functions for filter window bank. Journal of Industrial & Management Optimization, 2017, 13 (5) : 0-0. doi: 10.3934/jimo.2020014
[14]

Kazimierz Malanowski, Helmut Maurer. Sensitivity analysis for state constrained optimal control problems. Discrete & Continuous Dynamical Systems - A, 1998, 4 (2) : 241-272. doi: 10.3934/dcds.1998.4.241
[15]

Qiang Du, Jingyan Zhang. Asymptotic analysis of a diffuse interface relaxation to a nonlocal optimal partition problem. Discrete & Continuous Dynamical Systems - A, 2011, 29 (4) : 1443-1461. doi: 10.3934/dcds.2011.29.1443
[16]

Leszek Gasiński, Nikolaos S. Papageorgiou. Relaxation of optimal control problems driven by nonlinear evolution equations. Evolution Equations & Control Theory, 2019, 0 (0) : 0-0. doi: 10.3934/eect.2020050
[17]

Mohsen Abdolhosseinzadeh, Mir Mohammad Alipour. Design of experiment for tuning parameters of an ant colony optimization method for the constrained shortest Hamiltonian path problem in the grid networks. Numerical Algebra, Control & Optimization, 2019, 0 (0) : 0-0. doi: 10.3934/naco.2020028
[18]

Lili Chang, Wei Gong, Guiquan Sun, Ningning Yan. PDE-constrained optimal control approach for the approximation of an inverse Cauchy problem. Inverse Problems & Imaging, 2015, 9 (3) : 791-814. doi: 10.3934/ipi.2015.9.791
[19]

Benedetto Piccoli. Optimal syntheses for state constrained problems with application to optimization of cancer therapies. Mathematical Control & Related Fields, 2012, 2 (4) : 383-398. doi: 10.3934/mcrf.2012.2.383
[20]

Piernicola Bettiol. State constrained $L^\infty$ optimal control problems interpreted as differential games. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 3989-4017. doi: 10.3934/dcds.2015.35.3989

 Impact Factor: 

Tools

Metrics

  • PDF downloads (13)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences