American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Semicontinuity of the solution set map to a set-valued weak vector variational inequality
  • JIMO Home
  • This Issue
  • Next Article
    Optimization of composition and processing parameters for alloy development: a statistical model-based approach
July  2007, 3(3): 503-517. doi: 10.3934/jimo.2007.3.503

Semilocally prequasi-invex functions and characterizations

Jin-bao Jian 1, , Hua-qin Pan 1, and  Han-jun Zeng 1,

1. 

College of Mathematics and Information Science, Guangxi University, 530004, Nanning, P.R., China, China, China

Received  August 2006 Revised  January 2007 Published  July 2007

In this paper, based on semilocal convexity, invexity and prequasi-invexity, a new kind of generalized convexity called (strictly/ semistrictly) semilocally prequasi-invex functions is presented, and some of their basic characterizations are discussed. Then, several necessary and sufficient conditions for the proposed generalized convexity are established. Finally, some important properties of the optimal solutions to the associated generalized convex optimization problems are discussed.
Keywords: locally invex set, semilocally prequasi-invex functions, prequasi-invex functions, generalized convexity..
Mathematics Subject Classification: 90C30, 90C53, 49M37, 65K10, 65K0.
Citation: Jin-bao Jian, Hua-qin Pan, Han-jun Zeng. Semilocally prequasi-invex functions and characterizations. Journal of Industrial & Management Optimization, 2007, 3 (3) : 503-517. doi: 10.3934/jimo.2007.3.503
[1]

Anurag Jayswal, Ashish Kumar Prasad, Izhar Ahmad. On minimax fractional programming problems involving generalized $(H_p,r)$-invex functions. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1001-1018. doi: 10.3934/jimo.2014.10.1001
[2]

Cai-Ping Liu. Some characterizations and applications on strongly $\alpha$-preinvex and strongly $\alpha$-invex functions. Journal of Industrial & Management Optimization, 2008, 4 (4) : 727-738. doi: 10.3934/jimo.2008.4.727
[3]

Jagannathan Gomatam, Isobel McFarlane. Generalisation of the Mandelbrot set to integral functions of quaternions. Discrete & Continuous Dynamical Systems - A, 1999, 5 (1) : 107-116. doi: 10.3934/dcds.1999.5.107
[4]

Ezzeddine Zahrouni. On the Lyapunov functions for the solutions of the generalized Burgers equation. Communications on Pure & Applied Analysis, 2003, 2 (3) : 391-410. doi: 10.3934/cpaa.2003.2.391
[5]

Tao Chen, Linda Keen. Slices of parameter spaces of generalized Nevanlinna functions. Discrete & Continuous Dynamical Systems - A, 2019, 39 (10) : 5659-5681. doi: 10.3934/dcds.2019248
[6]

Samir Hodžić, Enes Pasalic. Generalized bent functions -sufficient conditions and related constructions. Advances in Mathematics of Communications, 2017, 11 (3) : 549-566. doi: 10.3934/amc.2017043
[7]

Shingo Takeuchi. The basis property of generalized Jacobian elliptic functions. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2675-2692. doi: 10.3934/cpaa.2014.13.2675
[8]

Hiroyuki Kobayashi, Shingo Takeuchi. Applications of generalized trigonometric functions with two parameters. Communications on Pure & Applied Analysis, 2019, 18 (3) : 1509-1521. doi: 10.3934/cpaa.2019072
[9]

Limin Wen, Xianyi Wu, Xiaobing Zhao. The credibility premiums under generalized weighted loss functions. Journal of Industrial & Management Optimization, 2009, 5 (4) : 893-910. doi: 10.3934/jimo.2009.5.893
[10]

Mihaela Roxana Nicolai, Dan Tiba. Implicit functions and parametrizations in dimension three: Generalized solutions. Discrete & Continuous Dynamical Systems - A, 2015, 35 (6) : 2701-2710. doi: 10.3934/dcds.2015.35.2701
[11]

Xia Li, Yong Wang, Zheng-Hai Huang. Continuity, differentiability and semismoothness of generalized tensor functions. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020131
[12]

Sina Greenwood, Rolf Suabedissen. 2-manifolds and inverse limits of set-valued functions on intervals. Discrete & Continuous Dynamical Systems - A, 2017, 37 (11) : 5693-5706. doi: 10.3934/dcds.2017246
[13]

Mehar Chand, Jyotindra C. Prajapati, Ebenezer Bonyah, Jatinder Kumar Bansal. Fractional calculus and applications of family of extended generalized Gauss hypergeometric functions. Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : 539-560. doi: 10.3934/dcdss.2020030
[14]

Lijia Yan. Some properties of a class of $(F,E)$-$G$ generalized convex functions. Numerical Algebra, Control & Optimization, 2013, 3 (4) : 615-625. doi: 10.3934/naco.2013.3.615
[15]

Zhong-Qing Wang, Ben-Yu Guo, Yan-Na Wu. Pseudospectral method using generalized Laguerre functions for singular problems on unbounded domains. Discrete & Continuous Dynamical Systems - B, 2009, 11 (4) : 1019-1038. doi: 10.3934/dcdsb.2009.11.1019
[16]

H.Thomas Banks, Danielle Robbins, Karyn L. Sutton. Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1301-1333. doi: 10.3934/mbe.2013.10.1301
[17]

Leon Ehrenpreis. Special functions. Inverse Problems & Imaging, 2010, 4 (4) : 639-647. doi: 10.3934/ipi.2010.4.639
[18]

Nguyen Thi Bach Kim, Nguyen Canh Nam, Le Quang Thuy. An outcome space algorithm for minimizing the product of two convex functions over a convex set. Journal of Industrial & Management Optimization, 2013, 9 (1) : 243-253. doi: 10.3934/jimo.2013.9.243
[19]

Shay Kels, Nira Dyn. Bernstein-type approximation of set-valued functions in the symmetric difference metric. Discrete & Continuous Dynamical Systems - A, 2014, 34 (3) : 1041-1060. doi: 10.3934/dcds.2014.34.1041
[20]

Gregorio Díaz, Jesús Ildefonso Díaz. On the free boundary associated with the stationary Monge--Ampère operator on the set of non strictly convex functions. Discrete & Continuous Dynamical Systems - A, 2015, 35 (4) : 1447-1468. doi: 10.3934/dcds.2015.35.1447

2019 Impact Factor: 1.366

Tools

Metrics

  • PDF downloads (34)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences