Optimality conditions and duality models for a class of nonsmooth constrained fractional variational problems

DOI10.1080/02331939408843969zbMath0818.90134OpenAlexW2017533061MaRDI QIDQ4764856

G. J. Zalmai

Publication date: 20 April 1995

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331939408843969

zbMATH Keywords

constrained variational problemsfractional objective functionarbitrary normsparametric and nonparametric necessary and sufficient optimality conditionssmooth and nonsmooth finite-dimensional nonlinear programming

Mathematics Subject Classification ID

Nonlinear programming (90C30) Variational inequalities (49J40) Nonsmooth analysis (49J52) Fractional programming (90C32) Programming in abstract spaces (90C48) Duality theory (optimization) (49N15)

Related Items

Sufficient optimality criteria and duality for nondifferentiable fractional variational problems with generalized (F, ρ)-convexity ⋮ A fifth bibliography of fractional programming^* ⋮ OPTIMALITY CONDITIONS AND DUALITY MODELS FOR A CLASS OF NONSMOOTH CONTINUOUS-TIME GENERALIZED FRACTIONAL PROGRAMMING PROBLEMS ⋮ Optimality conditions and duality models for a class of nonsmooth constrained fractional optimal control problems ⋮ Generalized \((\eta,\rho)\)-invex functions and global semiparametric sufficient efficiency conditions for multiobjective fractional programming problems containing arbitrary norms ⋮ Generalized \((\eta,\rho)\)-invex functions and semiparametric duality models for multiobjective fractional programming problems containing arbitrary norms ⋮ Generalized parameter-free duality models in discrete minmax fractional programming based on second-order optimality conditions ⋮ Global parametric sufficient optimality conditions for discrete minmax fractional programming problems containing generalized \((\theta,\eta,\rho)\)-V-invex functions and arbitrary norms ⋮ Duality for nondifferentiable static multiobjective variational problems involving generalized \((F,\rho)\)-convex functions ⋮ Existence of solutions for nonlinear fractional \(q\)-difference integral equations with two fractional orders and nonlocal four-point boundary conditions ⋮ Duality for a fractional variational formulation using $\eta$-approximated method ⋮ On efficiency and duality for a class of nonconvex nondifferentiable multiobjective fractional variational control problems ⋮ Optimality and duality for generalized fractional variational problems involving generalized (fρ)-convex functions ⋮ Semiparametric proper efficiency conditions and duality models for a class of constrained multiobjective fractional variational problems containing arbitrary norms ⋮ Proper efficiency conditions and duality models for constrained multiobjective optimal control probelms containing arbitrary norms ⋮ Efficiency Criteria and Duality Models for Multiobjective Fractional Programming Problems Containing Locall'y Subdifferentiable and ρ-Convex Functions ⋮ Parametric duality models for discrete minmax fractional programming problems containing generalized \((\theta,\eta,\rho)\)-V-invex functions and arbitrary norms ⋮ Three types dual model for minimax fractional programming ⋮ Duality for variational problems with b-vex functions ⋮ Minmax programming problems with \(L_ p\)-norms via nonsmooth \(V\)-invexity. ⋮ Semiparametric sufficient efficiency conditions for multiobjective fractional programming problems containing arbitrary norms ⋮ Parameter-free dual models for fractional programming with generalized invexity ⋮ A taxonomy and review of the multi-objective fractional programming (MOFP) problems ⋮ Proper efficiency and duality for a class of constrained multiobjective fractional optimal control problems containing arbitrary norms ⋮ Optimality conditions and duality for multiobjective variational problems with generalized \(B\)-invexity ⋮ Optimality conditions and duality models for generalized fractional programming problems containing locally subdifferentiable and ρ:-convex functions ⋮ Semiparametric proper efficiency principles and duality models for constrained multiobjective fractional optimal control problems containing arbitrary norms.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nondifferentiable fractional programming with Hanson-Mond classes of functions
• Optimality conditions for fractional minmax programming
• A class of nondifferentiable continuous programming problems
• A class of nondifferentiable control problems
• Fractional programming - a survey
• Duality with invexity for a class of nondifferentiable static and continuous programming problems
• Nondifferentiable mathematical programming and convex-concave functions
• A duality theorem for a homogeneous fractional programming problem
• A subgradient duality theorem
• A system of inequalities and nondifferentiable mathematical programming
• A class of programming problems whose objective function contains a norm
• Symmetry and self-duality in nonlinear programming
• An extension of the transposition theorems of Farkas and Eisenberg
• A dual-linear program
• A duality theorem for a nondifferentiable nonlinear fractional programming problem
• On Duality for Fractional Programming
• On a complementarity problem associated with nondifferentiable programming
• Optimality conditions for a class of nondifferentiable minmax programming problems
• Supports of a convex function
• First and second order conditions for a class of nondifferentiable optimization problems
• On converse duality for a nondifferentiable program
• Symmetric dual nondifferentiable programs
• Bibliography in fractional programming
• Calculation of Investment Portfolios with Risk Free Borrowing and Lending
• Duality Theorems for Non‐Linear Fractional Programs
• Fractional Programming. I, Duality
• A Solvability Theorem for Homogeneous Functions
• A Duality Theorem for a Nondifferentiable Fractional Programming Problem
• Sufficient Fritz John optimality conditions for nondifferentiable convex programming
• A programming problem with an L_p norm in the objective function
• Symmetric Duality via Conjugate Duality
• On a constraint qualification in a nondifferentiable programming problem
• Optimality criteria for a class of non differentiable non-linear programs
• A Class of Nondifferentiable Fractional Programming Problems
• A note on duality in homogeneous fractional programming
• Optimality Criteria for a Class of Non‐differentiable Mathematical Programs
• A Gradient Inequality for a Class of Nondifferentiable Functions
• An Extension of a Theorem on Supports of a Convex Function
• A Duality Theorem for Nonlinear Programming
• A GENERALIZATION OF A THEOREM OF SINHA ON SUPPORTS OF A CONVEX FUNCTION1
• A Note on Duality Theorem for a Nonlinear Programming Problem
• A theorem on supports of a convex functional in a realBanach space
• On duality in linear fractional functionals programming
• Properties of a multifacility location problem involving euclidian distances
• Technical Note—On a Duality Theorem for a Nonlinear Programming Problem
• Fractional programming
• Fractional programming