Necessary optimality conditions in terms of convexificators in Lipschitz optimization
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Publication:2370062
DOI10.1007/s10957-006-9155-zzbMath1143.90035OpenAlexW2036389630MaRDI QIDQ2370062
Publication date: 21 June 2007
Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10957-006-9155-z
constraint qualificationsconvexificatorsDini derivativesLocally Lipschitz functionsnecessary optimality conditions, nonsmooth optimizations
Minimax problems in mathematical programming (90C47) Optimality conditions and duality in mathematical programming (90C46) Nonsmooth analysis (49J52)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Convexifactors, generalized convexity, and optimality conditions
- General constraint qualifications in nondifferentiable programming
- Remarks on convex cones
- A generalized derivative for calm and stable functions
- Generalized tangent cone and an optimization problem in a normed space
- On constraint qualification in multiobjective optimization problems: Semidifferentiable case
- Nonsmooth calculus, minimality, and monotonicity of convexificators
- Error bounds for generalized Lagrange multipliers in locally Lipschitz programming
- Constrained qualifications in multiobjective optimization problems: Differentiable case
- Constraint qualifications and Lagrange multipliers in nondifferentiable programming problems
- Hunting for a smaller convex subdifferential
- Generalized properly efficient solutions of vector optimization problems
- Constraint qualifications in nonsmooth multiobjective optimization
- The Fritz John necessary optimality conditions in the presence of equality and inequality constraints
- Linear equations and inequalities on finite dimensional, real or complex, vector spaces: a unified theory
- Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives
- Nonsmooth Equations: Motivation and Algorithms
- Optimization and nonsmooth analysis
- Cores of Tangent Cones and Clarke's Tangent Cone
- Approximate subdifferentials and applications II
- On optimality conditions in nonsmooth inequality constrained minimization
- Convex Subcones of the Contingent Cone in Nonsmooth Calculus and Optimization
- On conditions to have bounded multipliers in locally lipschitz programming
- A necessary and sufficient regularity condition to have bounded multipliers in nonconvex programming
- On optimality conditions in nondifferentiable programming
- Approximate Jacobian Matrices for Nonsmooth Continuous Maps and C1-Optimization
- Approximate generalized Hessians and Taylor’s expansions for continuously Gâteaux differentiable functions
- Approximate Hessian matrices and second-order optimality conditions for nonlinear programming problems with C1-data
- A Sharp Lagrange Multiplier Rule for Nonsmooth Mathematical Programming Problems Involving Equality Constraints
- A Multiplier Rule for Multiobjective Programming Problems with Continuous Data
- The Linear Nonconvex Generalized Gradient and Lagrange Multipliers
- Convex Analysis
- A Necessary and Sufficient Qualification for Constrained Optimization
- Constraint Qualifications Revisited
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