拟凸规划近似解的特征刻画和近似对偶理论

RichHTML

PDF (PC)

Characterizations of Approximate Solution and Approximate Duality for Quasiconvex Programming

Abstract

References 31

Metrics

Comments

Recommended 10

Abstract

Cite this article

share this article

References 31

Related Articles 1

Metrics

Comments

Recommended 10

Abstract:

By using the properties of the approximate subdifferentials of involved functions and generators of quasiconvex functions, we introduce a new constraint qualification. Under this constraint qualification, characterizations of the quasi $(\alpha,\varepsilon)$ -optimal solution, the approximate saddle point theorems and the approximate mixed type duality theorems for quasiconvex programming are established.

Key words: quasiconvex programming, quasi $(\alpha,\varepsilon)$ -optimal solution, approximate saddle point theorem, mixed type duality

CLC Number:

O224

Donghui Fang,Junying Wang. Characterizations of Approximate Solution and Approximate Duality for Quasiconvex Programming[J].Acta mathematica scientia,Series A, 2025, 45(2): 640-652.

Trendmd

[1]	Boţ R I. Conjugate Duality in Convex Optimization. Berlin: Springer-Verlag, 2010
[2]	Dinh N, Goberna M A, López M A, et al. New Farkas-type constraint qualifications in convex infinite programming. ESAIM Control Optim Calc Var, 2007, 13: 580-597
[3]	Fang D H, Li C, Ng K F. Constraint qualifications for optimality conditions and total Lagrangian dualities in convex infinite programming. Nonlinear Anal, 2010, 73: 1143-1159
[4]	袁亚湘, 孙文瑜. 最优化理论与方法. 北京: 科学出版社, 1997
	Yuan Y X, Sun W Y. Optimization Theory and Methods. Beijing: Science Press, 1997
[5]	Zălinescu C. Convex Analysis in General Vector Spaces. New Jersey: World Scientific, 2002
[6]	Dinh N, Son T Q. Approximate optimality conditions and duality for convex infinite programming problems. J Sciences and Technology Development, 2007, 10: 29-38
[7]	Lee J H, Lee G M. On $\varepsilon$ -solutions for convex optimization problems with uncertainty data. Positivity, 2012, 16: 509-526
[8]	Long X J, Sun X K, Peng Z Y. Approximate optimality conditions for composite convex optimization problems. J Oper Res Soc China, 2017, 5: 469-485
[9]	Sun X K, Teo K L, Zeng J, Liu L Y. On approximate solutions and saddle point theorems for robust convex optimization. Optim Lett, 2020, 14: 1711-1730
[10]	Bae K D, Kim D S, Shitkovskaya G R P. $\varepsilon$ -wolfe type duality for convex optimization problems under data uncertainty. J Nonlinear Convex Anal, 2023, 24: 2573-2592
[11]	Jiao L G, Lee J H. Approximate optimality and approximate duality for quasi approximate solutions in robust convex semidefinite programs. J Optim Theory and Appl, 2018, 176: 74-93
[12]	Lee J H, Jiao L G. On quasi $\varepsilon$ -solution for robust convex optimization problems. Optim Lett, 2017, 11: 1609-1622
[13]	Fang D H, Wang J L, Wang X Y, Wen C F. Optimality conditions of quasi $(\alpha,\varepsilon)$ -solutions and approximate mixed type duality for DC composite optimization problems. J Nonlinear Var Anal, 2023, 7: 129-143
[14]	Jiao L G, Kim D S. Optimality conditions for quasi $(\alpha,\varepsilon)$ -solutions in convex optimization problems under data uncertainty. J Nonlinear Convex Anal, 2019, 2112: 73-79
[15]	Wang J L, Xie F F, Wang X Y, Fang D H. Approximate optimality conditions and mixed type duality for composite convex optimization problems. J Nonlinear Convex Anal, 2022, 23: 755-768
[16]	Boţ R I, Grad S M. Wolfe duality and Mond-Weir duality via perturbations. Nonlinear Anal, 2010, 73: 374-384
[17]	Sun X K, Li X B, Long X J, Peng Z Y. On robust approximate optimal solutions for uncertain convex optimization and applications to multi-objective optimization. Pac J Optim, 2017, 13: 621-643
[18]	Bector C R, Abha S C. On mixed duality in mathematical programming. Math Anal Appl, 2001, 259: 346-356
[19]	Sun X K, Teo K L, Tang L P. Dual approaches to characterize robust optimal solution sets for a class of uncertain optimization problems. J Optim Theory Appl, 2019, 182: 984-1000
[20]	Wang J Y, Fang D H, Qiu L X, Zeng Z H. Approximate optimality conditions and mixed type duality for quasiconvex optimization problems. J Nonlinear Convex Anal, 2024, 25: 155-167
[21]	Liu J, Long X J, Huang N J. Approximate optimality conditions and mixed type duality for semi-infinite multiobjective programming problems involving tangential subdifferentials. J Ind Manag Optim, 2023, 19: 6500-6519
[22]	Fang D H, Luo X F, Wang X Y. Strong and total lagrange dualities for quasiconvex programming. J Appl Math, 2014, 2014: 1-8
[23]	Fang D H, Yang T, Liou Y C. Strong and total Lagrange dualities for quasiconvex programming. J Nonlinear Var Anal, 2022, 6: 1-15
[24]	Suzuki S. Optimality conditions and constraint qualifications for quasiconvex programming. J Optim Theory and Appl, 2019, 183: 963-976
[25]	Suzuki S. Karush-Kuhn-Tucker type optimality condition for quasiconvex programming in terms of Greenberg-Pierskalla subdifferential. J Glob Optim, 2021, 79: 191-202
[26]	Zhao X P. On constraint qualification for an infinite system of quasiconvex inequalities in normed linear space. Taiwanese J Math, 2016, 20: 685-697
[27]	Fang D H, Qiu L X, Wang J Y, Wen C F. On constraint qualifications for an infinite system of quasiconvex inequalifies. J Nonlinear Var Anal, 2024, 8: 305-14
[28]	Dempe S, Gadhi N, Hamdaoui K. Minimizing the difference of two quasiconvex functions. Optim Lett, 2020, 14: 1765-1779
[29]	Penot J P, Volle M. On quasi-convex dualitys. Math Oper Res, 1990, 15: 597-625
[30]	Suzuki S, Kuroiwa D. On set containment characterization and constraint qualification for quasiconvex programming. J Optim Theory Appl, 2011, 149: 554-563
[31]	Suzuki S, Kuroiwa D. Generators and constraint qualifications for quasiconvex inequality systems. J Nonlinear Convex Anal, 2017, 18: 2101-2121

Viewed

Full text

From	Others	local

Times	2	75
Rate	3%	97%

Abstract

Just accepted	Online first	Issue

0	0	49

From	Others	local

Times	48	1
Rate	98%	2%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

Discussed

[1]	Ren Chenchen, Yang Sudan. Existence and Uniqueness of Solutions for Sub-Linear Heat Equations with Almost Periodic Coefficients[J]. Acta mathematica scientia,Series A, 2025, 45(1): 31 -43 .
[2]	Fu Yuechen, Ni Mingkang. The Inner Layer of a Class of Singularly Perturbed High-Order Equations with Discontinuous Right-Hand Side[J]. Acta mathematica scientia,Series A, 2024, 44(5): 1153 -1166 .
[3]	Zhang Wei, Chen Keyuan, Wu Yi, Ni Jinbo. Lyapunov-Type Inequalities for Dirichlet Problems of Multi-Term Caputo Fractional Differential Equations[J]. Acta mathematica scientia,Series A, 2024, 44(6): 1433 -1444 .
[4]	Yang Guicheng, Wen Yangzhe, Mao Jing. A Universal Inequality for the Dirichlet Eigenvalue Problem of the Weighted Laplacian and its Application[J]. Acta mathematica scientia,Series A, 2025, 45(1): 54 -73 .
[5]	Anqi Liu,Ting Yu,Changlin Xiang. Research on the Regularity of a Class of Biharmonic Map-Type Partial Differential Equation Systems[J]. Acta mathematica scientia,Series A, 2025, 45(2): 408 -417 .
[6]	Xiaoying Meng,Lu Lu. Existence and Asymptotic Behavior of Solutions for Kirchhoff Equations Involving the Fractional $p$ -Laplacian[J]. Acta mathematica scientia,Series A, 2025, 45(2): 434 -449 .
[7]	Xufei Lu,Changhua Jiao,Jinghua Yang. Affine Semigroup Dynamical Systems on $\mathbb{Z}_p$ [J]. Acta mathematica scientia,Series A, 2025, 45(2): 305 -320 .
[8]	Nizhou Li,Siyi Zhao,Jialing Zhang. Iteration of a Class of Separable Markov Mappings[J]. Acta mathematica scientia,Series A, 2025, 45(2): 321 -333 .
[9]	Yanxue Lin. Dynamical Localization for the CMV Matrices with Verblunsky Coeffcients Defined by the Skew-Shift[J]. Acta mathematica scientia,Series A, 2025, 45(2): 334 -346 .
[10]	Jianan Cui,Shugen Chai. Indirect Boundary Stabilization of Strongly Coupled Variable Coefficient Wave Equations[J]. Acta mathematica scientia,Series A, 2025, 45(2): 389 -407 .

Just accepted

Online first

Just accepted

Online first