Strongly Quasiconvex Functions: What We Know (So Far)
Author
Abstract
Suggested Citation
DOI: 10.1007/s10957-025-02641-4
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
References listed on IDEAS
- 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.
- Vial, Jean-Philippe, 1982. "Strong convexity of sets and functions," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 187-205, January.
- Mohsen Rahimi Piranfar & Hadi Khatibzadeh, 2021. "Long-Time Behavior of a Gradient System Governed by a Quasiconvex Function," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 169-191, January.
- Alfredo Iusem & Felipe Lara, 2019. "Optimality Conditions for Vector Equilibrium Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 187-206, January.
- 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.
- VIAL, Jean-Philippe, 1982. "Strong convexity of sets and functions," LIDAM Reprints CORE 475, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- J. P. Crouzeix & J. A. Ferland & C. Zălinescu, 1997. "(alpha)-Covex Sets and Strong Quasiconvexity," Mathematics of Operations Research, INFORMS, vol. 22(4), pages 998-1022, November.
- Yurii Nesterov, 2018. "Lectures on Convex Optimization," Springer Optimization and Its Applications, Springer, edition 2, number 978-3-319-91578-4, December.
- Hedy Attouch & Alexandre Cabot, 2020. "Convergence rate of a relaxed inertial proximal algorithm for convex minimization," Post-Print hal-02415789, HAL.
- Ion Necoara & Yurii Nesterov & François Glineur, 2019. "Linear convergence of first order methods for non-strongly convex optimization," LIDAM Reprints CORE 3000, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Alfredo Iusem & Felipe Lara, 2019. "Existence Results for Noncoercive Mixed Variational Inequalities in Finite Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 122-138, October.
- A. Kabgani & F. Lara, 2022. "Strong subdifferentials: theory and applications in nonconvex optimization," Journal of Global Optimization, Springer, vol. 84(2), pages 349-368, October.
- Chinedu Izuchukwu & Grace N. Ogwo & Yekini Shehu, 2024. "Proximal Point Algorithms with Inertial Extrapolation for Quasi-convex Pseudo-monotone Equilibrium Problems," Networks and Spatial Economics, Springer, vol. 24(3), pages 681-706, September.
- Diewert, W. E. & Avriel, M. & Zang, I., 1981. "Nine kinds of quasiconcavity and concavity," Journal of Economic Theory, Elsevier, vol. 25(3), pages 397-420, December.
- Felipe Lara & Rubén López, 2017. "Formulas for Asymptotic Functions via Conjugates, Directional Derivatives and Subdifferentials," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 793-811, June.
- Fabián Flores-Bazán & Fernando Flores-Bazán & Cristián Vera, 2015. "Maximizing and minimizing quasiconvex functions: related properties, existence and optimality conditions via radial epiderivatives," Journal of Global Optimization, Springer, vol. 63(1), pages 99-123, September.
- A. Iusem & F. Lara, 2022. "Proximal Point Algorithms for Quasiconvex Pseudomonotone Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 443-461, June.
- Alfredo Iusem & Felipe Lara, 2020. "A Note on “Existence Results for Noncoercive Mixed Variational Inequalities in Finite Dimensional Spaces”," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 607-608, November.
- G. Kassay & J. Kolumban, 2000. "Multivalued Parametric Variational Inequalities with α-Pseudomonotone Maps," Journal of Optimization Theory and Applications, Springer, vol. 107(1), pages 35-50, October.
- Shuvomoy Das Gupta & Bartolomeo Stellato & Bart P. G. Parys, 2024. "Exterior-Point Optimization for Sparse and Low-Rank Optimization," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 795-833, August.
- S.-M. Grad & F. Lara & R. T. Marcavillaca, 2023. "Relaxed-inertial proximal point type algorithms for quasiconvex minimization," Journal of Global Optimization, Springer, vol. 85(3), pages 615-635, March.
- 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.
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Sorin-Mihai Grad & Felipe Lara & Raúl Tintaya Marcavillaca, 2024. "Relaxed-Inertial Proximal Point Algorithms for Nonconvex Equilibrium Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 203(3), pages 2233-2262, December.
- A. Iusem & F. Lara, 2022. "Proximal Point Algorithms for Quasiconvex Pseudomonotone Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 443-461, June.
- Alfredo Iusem & Felipe Lara & Raúl T. Marcavillaca & Le Hai Yen, 2024. "A Two-Step Proximal Point Algorithm for Nonconvex Equilibrium Problems with Applications to Fractional Programming," Journal of Global Optimization, Springer, vol. 90(3), pages 755-779, November.
- Felipe Lara & Raúl T. Marcavillaca & Phan Tu Vuong, 2025. "Characterizations, Dynamical Systems and Gradient Methods for Strongly Quasiconvex Functions," Journal of Optimization Theory and Applications, Springer, vol. 206(3), pages 1-25, September.
- S.-M. Grad & L. D. Muu & T. V. Thang, 2025. "Proximal-Type Algorithms for Solving Nonconvex Mixed Multivalued Quasi-Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 206(2), pages 1-26, August.
- Chinedu Izuchukwu & Yekini Shehu & Chibueze C. Okeke, 2023. "Extension of forward-reflected-backward method to non-convex mixed variational inequalities," Journal of Global Optimization, Springer, vol. 86(1), pages 123-140, May.
- S.-M. Grad & F. Lara & R. T. Marcavillaca, 2023. "Relaxed-inertial proximal point type algorithms for quasiconvex minimization," Journal of Global Optimization, Springer, vol. 85(3), pages 615-635, March.
- A. Kabgani & F. Lara, 2022. "Strong subdifferentials: theory and applications in nonconvex optimization," Journal of Global Optimization, Springer, vol. 84(2), pages 349-368, October.
- Giorgi Giorgio, 2018. "A Classroom Note on Twice Continuously Differentiable Strictly Convex and Strongly Quasiconvex Functions," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(3), pages 42-52, June.
- Felipe Lara, 2020. "Optimality Conditions for Nonconvex Nonsmooth Optimization via Global Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 134-150, April.
- Tran Thang & Xuan Thanh Le, 2024. "Self-Adaptive Extragradient Algorithms for Quasi-Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 203(3), pages 2988-3013, December.
- 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.
- Chinedu Izuchukwu & Grace N. Ogwo & Yekini Shehu, 2024. "Proximal Point Algorithms with Inertial Extrapolation for Quasi-convex Pseudo-monotone Equilibrium Problems," Networks and Spatial Economics, Springer, vol. 24(3), pages 681-706, September.
- Shenghua Wang & Ziqi Zhu & Lanxiang Yu, 2025. "Stochastic golden ratio algorithm to non-convex stochastic mixed variational inequality problem," Journal of Global Optimization, Springer, vol. 91(4), pages 829-850, April.
- D. H. Yuan & X. L. Liu & A. Chinchuluun & P. M. Pardalos, 2006. "Nondifferentiable Minimax Fractional Programming Problems with (C, α, ρ, d)-Convexity," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 185-199, April.
- Thai Doan Chuong & José Vicente-Pérez, 2025. "Conic relaxations for conic minimax convex polynomial programs with extensions and applications," Journal of Global Optimization, Springer, vol. 91(4), pages 743-763, April.
- 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.
- Yboon García & Bruno Goicochea & Rubén López & Javier Martínez, 2025. "Horizon and Recession Asymptotic Notions for Sets and Mappings: A Unified Approach," Journal of Optimization Theory and Applications, Springer, vol. 205(2), pages 1-31, May.
- Nicolas Hadjisavvas & Felipe Lara & Dinh The Luc, 2020. "A general asymptotic function with applications in nonconvex optimization," Journal of Global Optimization, Springer, vol. 78(1), pages 49-68, September.
- 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.
More about this item
Keywords
Strongly quasiconvex functions; Proximal point algorithms; Equilibrium problems; Nonconvex optimization; Subgradient methods;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:205:y:2025:i:2:d:10.1007_s10957-025-02641-4. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.