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Beyond Convexity: New Perspectives in Computational Optimization

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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

For computational solutions of convex optimization problems, a rich body of knowledge including theory, algorithms, and computational experience is now available. In contrast, nothing of comparable depth and completeness can be offered at the present time, for non-convex problems. The field of convex optimization benefited immensely from pre-existing body of concepts and knowledge from pure mathematics, while non-convex problems seems to require formulation and exploration of entirely new mathematical concepts, as well as new models of computation. The intent of this paper is to describe our efforts in this direction, at a philosophical or conceptual level, without going into specific applications or implementation in software. We also point out connections with other areas, particularly mathematical physics.

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Author information

Authors and Affiliations

  1. Laboratory for Computational Mathematics, USA

    Narendra Karmarkar

Authors
  1. Narendra Karmarkar
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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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Karmarkar, N. (2010). Beyond Convexity: New Perspectives in Computational Optimization. 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_1

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  • DOI: https://doi.org/10.1007/978-3-642-17298-4_1

  • 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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