The KKT optimality conditions in a class of generalized convex optimization problems with an interval-valued objective function

DOI10.1007/s11590-012-0601-6zbMath1317.90240OpenAlexW2032705969MaRDI QIDQ2448142

Quanxi Feng, Lifeng Li, Jianke Zhang, San-Yang Liu

Publication date: 30 April 2014

Published in: Optimization Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11590-012-0601-6

zbMATH Keywords

Karush-Kuhn-Tucker optimality conditionsinterval-valued functionsHukuhara difference

Mathematics Subject Classification ID

Convex programming (90C25) Optimality conditions and duality in mathematical programming (90C46)

Related Items (34)

On interval-valued invex mappings and optimality conditions for interval-valued optimization problems ⋮ An exact \(l_1\) penalty approach for interval-valued programming problem ⋮ KKT optimality conditions in interval valued multiobjective programming with generalized differentiable functions ⋮ Saddle-point optimality criteria involving (p, b, d)-invexity and (p, b, d)-pseudoinvexity in interval-valued optimisation problems ⋮ The KKT optimality conditions for optimization problem with interval-valued objective function on Hadamard manifolds ⋮ Necessary optimality conditions for interval optimization problems with functional and abstract constraints ⋮ The \(F\)-objective function method for differentiable interval-valued vector optimization problems ⋮ On fuzzy generalized convex mappings and optimality conditions for fuzzy weakly univex mappings ⋮ Optimality conditions for interval valued optimization problems ⋮ Optimality conditions for fuzzy optimization problems under granular convexity concept ⋮ Interval-valued programming problem with infinite constraints ⋮ A class of nonconvex fuzzy optimization problems under granular differentiability concept ⋮ Two classes of granular solutions and related optimality conditions for interval type-2 fuzzy optimization ⋮ On preinvex interval-valued functions and unconstrained interval-valued optimization problems ⋮ Optimality conditions for a class ofE-differentiable vector optimization problems with interval-valued objective functions underE-invexity ⋮ On characterizations of solution sets of interval-valued quasiconvex programming problems ⋮ Interval order relationships based on automorphisms and their application to interval optimization ⋮ On interval-valued optimization problems with generalized invex functions ⋮ Solving interval quadratic programming problems by using the numerical method and swarm algorithms ⋮ On some characterizations of preinvex fuzzy mappings ⋮ Extended Karush-Kuhn-Tucker condition for constrained interval optimization problems and its application in support vector machines ⋮ On interval-valued pseudolinear functions and interval-valued pseudolinear optimization problems ⋮ Nonsmooth interval-valued optimization and saddle-point optimality criteria ⋮ Optimality conditions for \(E\)-differentiable vector optimization problems with the multiple interval-valued objective function ⋮ A saddle point characterization of efficient solutions for interval optimization problems ⋮ Relationships between interval-valued vector optimization problems and vector variational inequalities ⋮ Sufficiency and duality in non-smooth interval valued programming problems ⋮ Optimality conditions for interval-valued univex programming ⋮ On semidifferentiable interval-valued programming problems ⋮ Sufficient optimality criteria for optimization problem involving pseudoconvex interval objective function ⋮ New efficiency conditions for multiobjective interval-valued programming problems ⋮ Optimality, duality and saddle point analysis for interval-valued nondifferentiable multiobjective fractional programming problems ⋮ Optimality and duality for second-order interval-valued variational problems ⋮ Relations between multidimensional interval-valued variational problems and variational inequalities

Cites Work

• Unnamed Item
• Unnamed Item
• Duality theory in interval-valued linear programming problems
• Invexity and optimization
• Duality theory for optimization problems with interval-valued objective functions
• Wolfe duality for interval-valued optimization
• Pre-invex functions in multiple objective optimization
• On sufficiency of the Kuhn-Tucker conditions
• Multiobjective programming in optimization of interval objective functions -- a generalized approach
• On invex sets and preinvex functions
• The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions
• The Karush--Kuhn--Tucker optimality conditions in an optimization problem with interval-valued objective function
• Posynomial geometric programming with interval exponents and coefficients
• A nonlinear interval number programming method for uncertain optimization problems
• On interval-valued nonlinear programming problems
• Multiobjective programming in optimization of the interval objective function
• Invexity and generalized convexity
• What is invexity?
• A class of nonconvex functions and mathematical programming
• A variational-like inequality problem
• A Decomposition Method for Interval Linear Programming
• Characterizations and applications of prequasi-invex functions.

This page was built for publication: The KKT optimality conditions in a class of generalized convex optimization problems with an interval-valued objective function