Citations (61)
Keep up to date with the latest research on this topic with citation updates for this article.
Read on this site (10)
Giancarlo Bigi, Adela Capătă & Gábor Kassay. (2012) Existence results for strong vector equilibrium problems and their applications. Optimization 61:5, pages 567-583.
Read now
Read now
Do Van Luu & Nguyen Manh Hung. (2009) On alternative theorems and necessary conditions for efficiency. Optimization 58:1, pages 49-62.
Read now
Read now
Anjana Gupta, Davinder Bhatia & Aparna Mehra. (2007) Higher Order Efficiency, Saddle Point Optimality, and Duality for Vector Optimization Problems. Numerical Functional Analysis and Optimization 28:3-4, pages 339-352.
Read now
Read now
S. Chandra, J. Dutta & C. S. Lalitha. (2004) Regularity Conditions and Optimality in Vector Optimization. Numerical Functional Analysis and Optimization 25:5-6, pages 479-501.
Read now
Read now
Sándor Komlósi. (2002) Farkas theorems for positively homogeneous quasiconvex functions. Journal of Statistics and Management Systems 5:1-3, pages 107-123.
Read now
Read now
A.J.V Brando,
M.A Rojas-Medar &
G.N Silva. (2000) Invex nonsmooth alternative theorem and applications
. Optimization 48:2, pages 239-253.
Read now
Read now
J. Dutta,
V. Vetrivel &
S. Nanda. (1997) On saddle points and optima for non-smooth and non-convex programs. Optimization 42:1, pages 71-83.
Read now
Read now
V. Preda. (1996) Optimality conditions and duality in multiple objective programming involving semilocally convex and related functions. Optimization 36:3, pages 219-230.
Read now
Read now
V. Jeyakumar. (1988) Non-convex infinite games. Optimization 19:2, pages 289-296.
Read now
Read now
B.D. Craven,
J. Gwinner &
V. Jeyakumar. (1987) Nonconvex theorems of the alternative and minimization. Optimization 18:2, pages 151-163.
Read now
Read now
Articles from other publishers (51)
Omar Benslimane, Nazih Abderrazzak Gadhi & Imad Amrani Zerrifi. (2024) <i>ε</i>-weak Pareto minimality in D. C. vector optimization. Numerical Algebra, Control and Optimization 0:0, pages 0-0.
Crossref
Crossref
Renying Zeng. (2023) Constraint Qualifications for Vector Optimization Problems in Real Topological Spaces. Axioms 12:8, pages 783.
Crossref
Crossref
Renying Zeng. (2023) On Sub Convexlike Optimization Problems. Mathematics 11:13, pages 2928.
Crossref
Crossref
Ahmed Roubi. (2022) Theorems of the Alternative Revisited and Some Extensions of Yuan’s Lemma. Set-Valued and Variational Analysis 30:3, pages 1213-1232.
Crossref
Crossref
Ying Gao, Rui-Xue Yue & Li-Ping Tang. (2021) Scalarization and Optimality Conditions for the Approximate Solutions to Vector Variational Inequalities in Banach Spaces. Bulletin of the Iranian Mathematical Society 48:1, pages 165-186.
Crossref
Crossref
Eero V. Tamminen. (2019) Strong Lagrange duality and the maximum principle for nonlinear discrete time optimal control problems. ESAIM: Control, Optimisation and Calculus of Variations 25, pages 20.
Crossref
Crossref
Surjeet Kaur Suneja, Sunila Sharma & Mamta Chaudhary. (2018) Vector optimization with generalized cone locally connected functions. OPSEARCH 55:2, pages 302-319.
Crossref
Crossref
Nicolae Popovici. (2015) A decomposition approach to vector equilibrium problems. Annals of Operations Research 251:1-2, pages 105-115.
Crossref
Crossref
J. Li & G. Mastroeni. (2016) Image Convexity of Generalized Systems with Infinite-Dimensional Image and Applications. Journal of Optimization Theory and Applications 169:1, pages 91-115.
Crossref
Crossref
Ying Gao, Xinmin Yang, Jin Yang & Hong Yan. (2015) Scalarizations and Lagrange multipliers for
approximate solutions in the vector optimization problems with
set-valued maps. Journal of Industrial & Management Optimization 11:2, pages 673-683.
Crossref
Crossref
Li-Ping Pang, Fan-Yun Meng, Shuang Chen & Dan Li. (2014) Optimality Conditions for Multiobjective Optimization Problem Constrained by Parameterized Variational Inequalities. Set-Valued and Variational Analysis 22:2, pages 285-298.
Crossref
Crossref
S. K. Suneja & Bhawna Kohli. (2012) Generalized nonsmooth cone convexity in terms of convexifactors in vector optimization. OPSEARCH 50:1, pages 89-105.
Crossref
Crossref
Giorgio Giorgi. (2013) A Note on the Guignard Constraint Qualification and the Guignard Regularity Condition in Vector Optimization. Applied Mathematics 04:04, pages 734-740.
Crossref
Crossref
C. P. Liu, H. W. J. Lee & X. M. Yang. (2011) Optimality conditions and duality on approximate solutions in vector optimization with arcwise connectivity. Optimization Letters 6:8, pages 1613-1626.
Crossref
Crossref
Nicolae Popovici & Matteo Rocca. (2012) Decomposition of generalized vector variational inequalities. Nonlinear Analysis: Theory, Methods & Applications 75:3, pages 1516-1523.
Crossref
Crossref
Giandomenico Mastroeni. 2012. Recent Developments in Vector Optimization. Recent Developments in Vector Optimization
169
220
.
Radu Ioan Boţ & Adela Elisabeta Capătă. (2010) Existence results and gap functions for the generalized equilibrium problem with composed functions. Nonlinear Analysis: Theory, Methods & Applications 72:1, pages 316-324.
Crossref
Crossref
X. Q. Yang & X. Y. Zheng. (2007) Approximate solutions and optimality conditions of vector variational inequalities in Banach spaces. Journal of Global Optimization 40:1-3, pages 455-462.
Crossref
Crossref
Franco Giannessi. 2009. Encyclopedia of Optimization. Encyclopedia of Optimization
3895
3902
.
B. D. Craven. 2009. Encyclopedia of Optimization. Encyclopedia of Optimization
1770
1774
.
P. H. Sach. (2007) Moreau–Rockafellar Theorems for Nonconvex Set-Valued Maps. Journal of Optimization Theory and Applications 133:2, pages 213-227.
Crossref
Crossref
R. Zeng & R. J. Caron. (2006) Generalized Motzkin Theorems of the Alternative and Vector Optimization Problems. Journal of Optimization Theory and Applications 131:2, pages 281-299.
Crossref
Crossref
Miguel Adán & Vicente Novo. (2005) Duality and saddle-points for convex-like vector optimization problems on real linear spaces. Top 13:2, pages 343-357.
Crossref
Crossref
P. H. Sach. (2005) New Generalized Convexity Notion for Set-Valued Maps and Application to Vector Optimization. Journal of Optimization Theory and Applications 125:1, pages 157-179.
Crossref
Crossref
. 2005. Constrained Optimization and Image Space Analysis. Constrained Optimization and Image Space Analysis
251
306
.
Nguyen Dinh, Gue Myung Lee & Anh Le Tuan. 2005. Continuous Optimization. Continuous Optimization
293
319
.
. 2004. Mathematics of Optimization. Mathematics of Optimization
201
358
.
Vasile Preda. (2003) Optimality and duality in fractional multiple objective programming involving semilocally preinvex and related functions. Journal of Mathematical Analysis and Applications 288:2, pages 365-382.
Crossref
Crossref
P. H. Sach. (2003) Nearly Subconvexlike Set-Valued Maps and Vector Optimization Problems. Journal of Optimization Theory and Applications 119:2, pages 335-356.
Crossref
Crossref
M. Adán & V. Novo. (2003) Weak efficiency in vector optimization using a closure of algebraic type under cone-convexlikeness. European Journal of Operational Research 149:3, pages 641-653.
Crossref
Crossref
J.Y. Fu & Y.H. Wang. (2003) Arcwise Connected Cone-Convex Functions and Mathematical Programming. Journal of Optimization Theory and Applications 118:2, pages 339-352.
Crossref
Crossref
S. K. Suneja & Seema Khurana. (2017) Saddle-Point Type Optimality Criteria for Optimization Problem over Cones. OPSEARCH 40:2, pages 81-96.
Crossref
Crossref
Sonia Davar & Aparna Mehra. (2001) Optimality Conditions and Duality for Fractional Programming Problems Involving Arcwise Connected Functions and Their Generalizations. Journal of Mathematical Analysis and Applications 263:2, pages 666-682.
Crossref
Crossref
Franco Giannessi. 2001. Encyclopedia of Optimization. Encyclopedia of Optimization
2611
2618
.
B. D. Craven. 2001. Encyclopedia of Optimization. Encyclopedia of Optimization
1172
1176
.
S. K. Suneja, S. Aggarwal & S. Davar. (2000) Generalized Connected Functions with Respect to Cones. Journal of Optimization Theory and Applications 106:2, pages 399-410.
Crossref
Crossref
G. Mastroeni & T. Rapcsák. (2000) On Convex Generalized Systems. Journal of Optimization Theory and Applications 104:3, pages 605-627.
Crossref
Crossref
D. Bhatia & A. Mehra. (1999) Optimality Conditions and Duality Involving Arcwise Connected and Generalized Arcwise Connected Functions. Journal of Optimization Theory and Applications 100:1, pages 181-194.
Crossref
Crossref
B. D. Craven & D. V. Luu. (2009) Lagrangian conditions for a nonsmooth vector-valued minimax. Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 65:2, pages 163-175.
Crossref
Crossref
W. Song. (1997) Lagrangian Duality for Minimization of Nonconvex Multifunctions. Journal of Optimization Theory and Applications 93:1, pages 167-182.
Crossref
Crossref
P. Q. Khanh. (1995) Sufficient optimality conditions and duality in vector optimization with invex-convexlike functions. Journal of Optimization Theory and Applications 87:2, pages 359-378.
Crossref
Crossref
P. Q. Khanh. (1995) Invex-convexlike functions and duality. Journal of Optimization Theory and Applications 87:1, pages 141-165.
Crossref
Crossref
E. V. Tamminen. (1994) Sufficient conditions for the existence of multipliers and Lagrangian duality in abstract optimization problems. Journal of Optimization Theory and Applications 82:1, pages 93-104.
Crossref
Crossref
V. Jeyakumar & X. Q. Yang. (1993) Convex composite multi-objective nonsmooth programming. Mathematical Programming 59:1-3, pages 325-343.
Crossref
Crossref
X.Q Yang & Guang-Ya Chen. (1992) A class of nonconvex functions and pre-variational inequalities. Journal of Mathematical Analysis and Applications 169:2, pages 359-373.
Crossref
Crossref
S. Paeck. (1992) Convexlike and concavelike conditions in alternative, minimax, and minimization theorems. Journal of Optimization Theory and Applications 74:2, pages 317-332.
Crossref
Crossref
V. Jeyakumar. (1991) Composite Nonsmooth Programming with Gâteaux Differentiability. SIAM Journal on Optimization 1:1, pages 30-41.
Crossref
Crossref
V. Jeyakumar & H. Wolkowicz. (1990) Zero duality gaps in infinite-dimensional programming. Journal of Optimization Theory and Applications 67:1, pages 87-108.
Crossref
Crossref
T. Weir & V. Jeyakumar. (2009) A class of nonconvex functions and mathematical programming. Bulletin of the Australian Mathematical Society 38:2, pages 177-189.
Crossref
Crossref
V Jeyakumar. (1988) Equivalence of saddle-points and optima, and duality for a class of non-smooth non-convex problems. Journal of Mathematical Analysis and Applications 130:2, pages 334-343.
Crossref
Crossref
F. Giannessi. (1987) Theorems of the alternative for multifunctions with applications to optimization: General results. Journal of Optimization Theory and Applications 55:2, pages 233-256.
Crossref
Crossref