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Interior proximal methods for quasiconvex optimization

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  • Nils Langenberg
  • Rainer Tichatschke

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  • Nils Langenberg & Rainer Tichatschke, 2012. "Interior proximal methods for quasiconvex optimization," Journal of Global Optimization, Springer, vol. 52(3), pages 641-661, March.
    • Handle: RePEc:spr:jglopt:v:52:y:2012:i:3:p:641-661
    DOI: 10.1007/s10898-011-9752-8
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    References listed on IDEAS

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    1. Nils Langenberg, 2010. "Pseudomonotone operators and the Bregman Proximal Point Algorithm," Journal of Global Optimization, Springer, vol. 47(4), pages 537-555, August.
    2. Jonathan Eckstein, 1993. "Nonlinear Proximal Point Algorithms Using Bregman Functions, with Applications to Convex Programming," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 202-226, February.
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    Cited by:

    1. Nils Langenberg, 2012. "An Interior Proximal Method for a Class of Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 902-922, December.
    2. H. Apolinário & E. Papa Quiroz & P. Oliveira, 2016. "A scalarization proximal point method for quasiconvex multiobjective minimization," Journal of Global Optimization, Springer, vol. 64(1), pages 79-96, January.
    3. Sorin-Mihai Grad & Felipe Lara, 2022. "An extension of the proximal point algorithm beyond convexity," Journal of Global Optimization, Springer, vol. 82(2), pages 313-329, February.
    4. Rocha, Rogério Azevedo & Oliveira, Paulo Roberto & Gregório, Ronaldo Malheiros & Souza, Michael, 2016. "Logarithmic quasi-distance proximal point scalarization method for multi-objective programming," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 856-867.
    5. Sorin-Mihai Grad & Felipe Lara, 2021. "Solving Mixed Variational Inequalities Beyond Convexity," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 565-580, August.
    6. Hugo Leiva & Nelson Merentes & Kazimierz Nikodem & José Sánchez, 2013. "Strongly convex set-valued maps," Journal of Global Optimization, Springer, vol. 57(3), pages 695-705, November.
    7. E. A. Papa Quiroz & S. Cruzado, 2022. "An inexact scalarization proximal point method for multiobjective quasiconvex minimization," Annals of Operations Research, Springer, vol. 316(2), pages 1445-1470, September.
    8. Xiaoqi Yang & Chenchen Zu, 2022. "Convergence of Inexact Quasisubgradient Methods with Extrapolation," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 676-703, June.
    9. F. Lara, 2022. "On Strongly Quasiconvex Functions: Existence Results and Proximal Point Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 891-911, March.

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