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Constrained Optimization

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Computer Vision

Synonyms

Constrained minimization

Related Concepts

Definition

Constrained optimization refers to the minimization of an objective function subject to hard constraint(s).

Background

Many computer vision problems have been resolved by mathematical optimization, where we try to optimize some criteria, called objective function, with or without hard constraint(s) that must be satisfied. This chapter focuses on constrained optimization, i.e., optimization problems involving hard constraint(s).

In general, constrained optimization is much more difficult than unconstrained one because algorithms must guarantee not only the convergence of the objective function to be minimized but also the satisfaction of given hard constraints. On the other hand, it has been recognized that the use of hard constraints brings various benefits, such as facilitating the choice of involved parameters and incorporating physical properties/structure directly on the solution, as addressed, for...

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References

  1. Afonso M, Bioucas-Dias J, Figueiredo M (2011) An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems. IEEE Trans Image Process 20(3):681–695

    Article  MathSciNet  Google Scholar 

  2. Bauschke HH, Combettes PL (2017) Convex analysis and monotone operator theory in Hilbert spaces, 2nd edn. Springer

    Book  Google Scholar 

  3. Boyd S, Parikh N, Chu E, Peleato B, Eckstein J (2011) Distributed optimization and statistical learning via the alternating direction method of multipliers. Found Trends Mach Learn 3(1):1–122

    Article  Google Scholar 

  4. Candès EJ, Li X, Ma Y, Wright J (2011) Robust principal component analysis? J ACM 58(3). https://doi.org/10.1145/1970392.1970395

  5. Chambolle A, Pock T (2010) A first-order primal-dual algorithm for convex problems with applications to imaging. J Math Imaging Vision 40(1):120–145

    Article  MathSciNet  Google Scholar 

  6. Chen H, Salman Asif M, Sankaranarayanan AC, Veeraraghavan A (2015) Fpa-cs: focal plane array-based compressive imaging in short-wave infrared. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

    Google Scholar 

  7. Chierchia G, Pustelnik N, Pesquet J-C, Pesquet-Popescu B (2014) Epigraphical projection and proximal tools for solving constrained convex optimization problems. Signal Image Video Process 9(8):1737–1749

    Article  Google Scholar 

  8. Combettes PL, Pesquet J-C (2011) Proximal splitting methods in signal processing. In: Bauschke HH et al (eds) Fixed-point algorithms for inverse problems in science and engineering. Springer, Springer-Verlag New York, pp 185–212

    Chapter  Google Scholar 

  9. Condat L (2016) Fast projection onto the simplex and the ℓ1 ball. Math Program 158(1–2):575–585

    Article  MathSciNet  Google Scholar 

  10. Duchi J, Shwartz SS, Singer Y, Chandra T (2008) Efficient projections onto the ℓ1-ball for learning in high dimensions. In: International Conference on Machine Learning, pp 272–279

    Google Scholar 

  11. Gabay D, Mercier B (1976) A dual algorithm for the solution of nonlinear variational problems via finite elements approximations. Comput Math Appl 2:17–40

    Article  Google Scholar 

  12. Ono S, Yamada I (2015) Signal recovery with certain involved convex data-fidelity constraints. IEEE Trans Signal Process 63(22):6149–6163

    Article  MathSciNet  Google Scholar 

  13. Ono S, Yamada I (2016) Color-line regularization for color artifact removal. IEEE Trans Comput Imag 2(3):204–217

    Article  MathSciNet  Google Scholar 

  14. Parikh N, Boyd S (2014) Proximal algorithms. Found Trends Optim 1(3):127–239

    Article  Google Scholar 

  15. Wright J, Ganesh A, Rao S, Peng Y, Ma Y (2009) Robust principal component analysis: exact recovery of corrupted low-rank matrices via convex optimization. In: Proceedings of Neural Information Processing Systems (NIPS), pp 2080–2088

    Google Scholar 

  16. Wu L, Ganesh A, Shi B, Matsushita Y, Wang Y, Ma Y (2010) Robust photometric stereo via low-rank matrix completion and recovery. In: Proceedings of the Asian Conference on Computer Vision (ACCV), pp 703–717

    Google Scholar 

  17. Zhang C, Liu J, Tian Q, Xu C, Lu H, Ma S (2011) Image classification by non-negative sparse coding, low-rank and sparse decomposition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp 1673–1680

    Google Scholar 

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Author information

Authors and Affiliations

  1. Tokyo Institute of Technology, Tokyo, Japan

    Shunsuke Ono

Authors
  1. Shunsuke Ono
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Corresponding author

Correspondence to Shunsuke Ono .

Section Editor information

  1. Department of Computer Science and Engineering, Waseda University, Tokyo, Japan

    Hiroshi Ishikawa

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Ono, S. (2020). Constrained Optimization. In: Computer Vision. Springer, Cham. https://doi.org/10.1007/978-3-030-03243-2_832-1

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  • DOI: https://doi.org/10.1007/978-3-030-03243-2_832-1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-03243-2

  • Online ISBN: 978-3-030-03243-2

  • eBook Packages: Springer Reference Computer SciencesReference Module Computer Science and Engineering

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