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A Parallel Algorithm for Solving Large Convex Minimax Problems

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Simulated Evolution and Learning (SEAL 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6457))

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Abstract

We consider unconstrained minimax problem where the objective function is the maximum of a finite number of smooth convex functions. We present an iterative method to compute the optimal solution for the unconstrained convex finite minimax problem. The algorithm developed estimates the direction of steepest-descent rapidly and using Armijo’s condition proceeds towards the solution. Owing to the highly parallel nature of the algorithm, it is highly suitable for large minimax problems. Algorithm is implemented on Nvidia Tesla C1060 graphics card using CUDA and numerical comparisons with RGA & CFSQP are presented.

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References

  1. Xu, S.: Smoothing Method for Minimax Problems. Computational Optimization and Applications 20, 267–279 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  2. Parpas, P., Rustem, B.: An Algorithm for the Global Optimization of a Class of Continuous Minimax Problems. Journal of Optimization Theory and Applications 141, 461–473 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Pillo, G.D., Grippo, L., Lucidi, S.: A Smooth Method for the Finite Minimax Problem. Math. Program. 60, 187–214 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  4. Rustem, B., Zakovic, S., Parpas, P.: An Interior Point Algorithm for Continuous Minimax. Journal of Optimization Theory and Applications 136, 87–103 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Polak, E., Womersley, R.S., Yin, H.X.: An Algorithm Based on Active Sets and Smoothing for Discretized Semi-Infinite Minimax Problems. Journal of Optimization Theory and Applications 138, 311–328 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Sun, W.: Non-Monotone Trust Region Method for Solving Optimization Problem. Applied Mathematics and Computation 156, 159–174 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  7. Charalamous, C., Conn, A.: An Efficient Method to Solve the Minimax Problem Directly. SIAM J. Numer. Anal. 15, 162–187 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  8. Chen, R.: Solution of Minimax Problem using Equivalent Differentiable Functions. Comp. and Maths. with Appls. 11, 1165–1169 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  9. Gaudioso, M., Monaco, M.F.: A Bundle Type Approach to the Unconstrained Minimization of Convex Non-Smooth Functions. Mathematical Programming 23, 216–226 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  10. Zhua, Z., Cai, X., Jian, J.: An Improved SQP Algorithm for Solving Minimax Problems. Applied Mathematical Letters 22, 464–469 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hiriart-Urruty, J.B., Lemarechal, C.: Convex Analysis and Minimization Algorithms I: Fundamentals. Springer, Heidelberg (1996)

    MATH  Google Scholar 

  12. Vardi, A.: New Minimax Algorithm. Journal of Optimization Theory and Applications (1992)

    Google Scholar 

  13. Wang, F., Zhang, K.: A Hybrid Algorithm for Nonlinear Minimax Problems. Annals of Operation Research (2008)

    Google Scholar 

  14. Goldberg, D.E.: Genetic Algorithms for Search, Optimization, and Machine Learning. Addison-Wesley, Reading (1989)

    MATH  Google Scholar 

  15. Deb, K., et al.: A Computationally Efficient Evolutionary Algorithm for Real-Parameter Optimization. Evol. Comput. 10(4), 371–395 (2002)

    Article  Google Scholar 

  16. Hansen, N., Muller, S., Koumoutsakos, P.: Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES). Evolutionary Computation 11(1), 1–18 (2003)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. The Courant Institute of Mathematical Sciences, New York University, USA

    Ramnik Arora

  2. The Department of Computer Science, EPFL, Lausanne, Switzerland

    Utkarsh Upadhyay

  3. The Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India

    Rupesh Tulshyan

  4. Indian Institute of Technology Kanpur, Kanpur, 208016, India

    J. Dutta

Authors
  1. Ramnik Arora
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  2. Utkarsh Upadhyay
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  3. Rupesh Tulshyan
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  4. J. Dutta
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Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Kanpur, 208016, Kanpur, Uttar Pradesh, India

    Kalyanmoy Deb

  2. Department of Computer Science andl Engineering, Indian Institute of Technology Kanpur, 208016, Kanpur, Uttar Pradesh, India

    Arnab Bhattacharya

  3. Department of Metallurgical and Materials Engineering, Indian Institute of Technology Kharagpur, 712302, Kharagpur, West Bengal, India

    Nirupam Chakraborti

  4. Department of Civil Engineering, Indian Institute of Technology Kanpur, 208016, Kanpur, Uttar Pradesh, India

    Partha Chakroborty  & Ashu Jain  & 

  5. Department of Electronics and Communication Engineering, Jadavpur University, 700032, Kolkata, West Bengal, India

    Swagatam Das

  6. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, 208016, Kanpur, Uttar Pradesh, India

    Joydeep Dutta

  7. Department of Chemical Engineering, Indian Institute of Technology Kanpur, 208016, Kanpur, Uttar Pradesh, India

    Santosh K. Gupta

  8. Aspiring Minds, 24 Pusa Road, 110005, New Delhi, India

    Varun Aggarwal

  9. Warwick Business School, University of Warwick, CV4 7AL, Coventry, UK

    Jürgen Branke

  10. Department of Computer Science and Engineering, University of Nevada, 89557, Reno, NV, USA

    Sushil J. Louis

  11. Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, 117576, Singapore

    Kay Chen Tan

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© 2010 Springer-Verlag Berlin Heidelberg

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Arora, R., Upadhyay, U., Tulshyan, R., Dutta, J. (2010). A Parallel Algorithm for Solving Large Convex Minimax Problems. In: Deb, K., et al. Simulated Evolution and Learning. SEAL 2010. Lecture Notes in Computer Science, vol 6457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17298-4_3

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  • DOI: https://doi.org/10.1007/978-3-642-17298-4_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17297-7

  • Online ISBN: 978-3-642-17298-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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