A class of programming problems whose objective function contains a norm

DOI10.1016/0021-9045(78)90091-6zbMath0398.41019OpenAlexW2011986332MaRDI QIDQ1254496

G. Alistair Watson

Publication date: 1978

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(78)90091-6

zbMATH Keywords

Constrained Best Approximation ProblemsOptimization AlgorithmsProgramming Problems

Mathematics Subject Classification ID

Nonlinear programming (90C30) Best approximation, Chebyshev systems (41A50) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Approximation with constraints (41A29)

Related Items (12)

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 ⋮ Global parametric sufficient optimality conditions for discrete minmax fractional programming problems containing generalized \((\theta,\eta,\rho)\)-V-invex functions and arbitrary norms ⋮ Best approximation with prescribed norm ⋮ 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 ⋮ On strong pseudoinvexity in a programming problem containing \(L_p\) norm in the objective function. ⋮ Minmax programming problems with \(L_ p\)-norms via nonsmooth \(V\)-invexity. ⋮ First and second order conditions for a class of nondifferentiable optimization problems ⋮ Optimality conditions and duality models for generalized fractional programming problems containing locally subdifferentiable and ρ:-convex functions ⋮ Optimality conditions and duality models for a class of nonsmooth constrained fractional variational problems ⋮ Generalized concavity and duality with a square root term

Cites Work

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• Symmetric duality, and a convergent subgradient method for discrete, linear, constrained approximation problems with arbitrary norms appearing in the objective function and in the constraints
• Algorithms for solving the dual problem for Av = b with varying norms
• A class of nondifferentiable mathematical programming problems
• Solutions of overdetermined linear equations which minimize error in an abstract norm
• Least squares algorithms for finding solutions of overdetermined linear equations which minimize error in an abstract norm
• On an algorithm for best approximate solutions to Av=b in normed linear spaces
• A programming problem with an L_p norm in the objective function

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