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Title of Journal: Math Program

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Abbravation: Mathematical Programming

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Springer Berlin Heidelberg

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DOI

10.1002/jrs.3003

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1436-4646

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Applications of convex analysis within mathematics

Authors: Francisco J Aragón Artacho Jonathan M Borwein Victoria MartínMárquez Liangjin Yao
Publish Date: 2013/08/30
Volume: 148, Issue: 1-2, Pages: 49-88
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Abstract

In this paper we study convex analysis and its theoretical applications We first apply important tools of convex analysis to Optimization and to Analysis We then show various deep applications of convex analysis and especially infimal convolution in Monotone Operator  Theory Among other things we recapture the Minty surjectivity theorem in Hilbert space and present a new proof of the sum theorem in reflexive spaces More technically we also discuss autoconjugate representers for maximally monotone operators Finally we consider various other applications in mathematical analysisThe authors are grateful to the three anonymous referees for their pertinent and constructive comments The authors also thank Dr Hristo S Sendov for sending them the manuscript 60 The authors were all partially supported by various Australian Research Council grants

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  1. Submodular maximization meets streaming: matchings, matroids, and more
  2. Some computationally relevant group theoretic structures of fixed charge problems
  3. Large-scale semidefinite programs in electronic structure calculation
  4. A distributionally robust perspective on uncertainty quantification and chance constrained programming
  5. The factorization approach to large-scale linear programming
  6. Beyond symmetric Broyden for updating quadratic models in minimization without derivatives
  7. A spatial branch-and-cut method for nonconvex QCQP with bounded complex variables
  8. Breakpoint searching algorithms for the continuous quadratic knapsack problem
  9. Sandwich games
  10. Approximations of Nash equilibria
  11. Using cuts for mixed integer knapsack sets to generate cuts for mixed integer polyhedral conic sets
  12. A robust and efficient method for solving point distance problems by homotopy
  13. A nonmonotone GRASP
  14. Extreme point inequalities and geometry of the rank sparsity ball
  15. Primal-dual interior-point methods for PDE-constrained optimization
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  17. Single item lot-sizing with non-decreasing capacities
  18. Structural and algorithmic properties for parametric minimum cuts
  19. Simple integer recourse models: convexity and convex approximations
  20. A model of the coNP-complete non-Hamilton tour decision problem for directed graphs
  21. Iteration complexity analysis of block coordinate descent methods
  22. Error Bounds of Regularized Gap Functions for Nonsmooth Variational Inequality Problems
  23. Accelerating the cubic regularization of Newton’s method on convex problems
  24. Bundle methods for sum-functions with “easy” components: applications to multicommodity network design
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  32. On some properties and an application of the logarithmic barrier method
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