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A Local Minimax Method Using Virtual Geometric Objects: Part II—For Finding Equality Constrained Saddles

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Abstract

Inspired by the method (Li, Ji and Zhou in J Sci Comput, 2018, https://doi.org/10.1007/s10915-018-0774-y) using a dynamics of points on virtual geometric objects containing a fixed local minimum and a flexible endpoint, but without knowing their explicit expressions or representative (interpolation) points, as a subsequent work presented in a self-contained manner, this paper is to develop a new local minimax method for finding equality constrained k-saddles of functionals with very different variational structures in infinite-dimensional spaces and to establish its mathematical justification including its strong dissipation law and convergence. Algorithm implementation is described by test problems in both finite and infinite dimensional spaces for computing equality constrained 1–2-saddles. Solutions are successfully computed and shown with their numerical data and profile-contour plots.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, China

    Zhaoxiang Li

  2. Department of Mathematics, Texas A&M University, College Station, TX, 77843, USA

    Jianxin Zhou

Authors
  1. Zhaoxiang Li
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  2. Jianxin Zhou
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Correspondence to Zhaoxiang Li or Jianxin Zhou.

Additional information

Z. Li: Supported in part by NSF of China (Nos. 11771298 and 11671251). J. Zhou: Supported in part by NSF Grant DMS-0311905.

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Li, Z., Zhou, J. A Local Minimax Method Using Virtual Geometric Objects: Part II—For Finding Equality Constrained Saddles. J Sci Comput 78, 226–245 (2019). https://doi.org/10.1007/s10915-018-0775-x

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  • DOI: https://doi.org/10.1007/s10915-018-0775-x

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