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Optimization and Real World Applications

Fixed Point Theory and Algorithms for Sciences and Engineering welcomes submissions to the Topical Collection on “Optimization and Real World Applications” edited by Heinz Bauschke, Yunier Bello-Cruz, Radu Ioan Bot, Robert Csetnek and Alexander Zaslavski, which covers a wide variety of topics concerning optimization problems and their applications. 

These include (but are not limited to) 
- smooth and nonsmooth optimization problems (theory and numerical methods), 
- monotone operators and nonexpansive mappings,
- real world applications in 
                    - machine learning,
                    - image/signal processing,
                    - data classification,
                    - scientific computing
and other areas.

Click the link below to download the PDF with all information on one page:

TC Optimization and Real World Applications

  1. The circumcentered-reflection method (CRM) has been applied for solving convex feasibility problems. CRM iterates by computing a circumcenter upon a composition of reflections with respect to convex sets. Sinc...

    Authors: G. H. M. Araújo, R. Arefidamghani, R. Behling, Y. Bello-Cruz, A. Iusem and L.-R. Santos
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2022 2022:1
  2. Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of...

    Authors: Pontus Giselsson and Walaa M. Moursi
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:25
  3. In 1990, Romero presented a beautiful formula for the projection onto the set of rectangular matrices with prescribed row and column sums. Variants of Romero’s formula were rediscovered by Khoury and by Glunt,...

    Authors: Heinz H. Bauschke, Shambhavi Singh and Xianfu Wang
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:23
  4. Inverse problems consist of recovering a signal from a collection of noisy measurements. These problems can often be cast as feasibility problems; however, additional regularization is typically necessary to e...

    Authors: Howard Heaton, Samy Wu Fung, Aviv Gibali and Wotao Yin
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:21
  5. By the first welfare theorem, competitive market equilibria belong to the core and hence are Pareto optimal. Letting money be a commodity, this paper turns these two inclusions around. More precisely, by generali...

    Authors: Sjur Didrik Flåm
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:20
  6. Splitting algorithms for finding a zero of sum of operators often involve multiple steps which are referred to as forward or backward steps. Forward steps are the explicit use of the operators and backward ste...

    Authors: Minh N. Dao and Hung M. Phan
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:16
  7. It is well known that the Newton method may not converge when the initial guess does not belong to a specific quadratic convergence region. We propose a family of new variants of the Newton method with the pot...

    Authors: Regina S. Burachik, Bethany I. Caldwell and C. Yalçın Kaya
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:15
  8. In this paper, we use a robust lower directional derivative and provide some sufficient conditions to ensure the strong regularity of a given mapping at a certain point. Then, we discuss the Hoffman estimation an...

    Authors: Malek Abbasi and Michel Théra
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:14
  9. We explore a new approach for training neural networks where all loss functions are replaced by hard constraints. The same approach is very successful in phase retrieval, where signals are reconstructed from m...

    Authors: Veit Elser
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:12
  10. This paper proposes a stochastic approximation method for solving a convex stochastic optimization problem over the fixed point set of a quasinonexpansive mapping. The proposed method is based on the existing ...

    Authors: Hideaki Iiduka
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:10
  11. String-averaging is an algorithmic structure used when handling a family of operators in situations where the algorithm in hand requires to employ the operators in a specific order. Sequential orderings are we...

    Authors: Yair Censor and Ariel Nisenbaum
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:9
  12. We propose Tseng’s extragradient methods for finding a solution of variational inequality problems associated with pseudomonotone vector fields in Hadamard manifolds. Under standard assumptions such as pseudom...

    Authors: Konrawut Khammahawong, Poom Kumam, Parin Chaipunya and Somyot Plubtieng
    Citation: Fixed Point Theory and Algorithms for Sciences and Engineering 2021 2021:5