A dual approach to constrained interpolation from a convex subset of Hilbert space

DOI10.1006/jath.1996.3082zbMath0884.41019OpenAlexW2070409288MaRDI QIDQ1369249

Frank Deutsch, Wu Li, Joseph D. Ward

Publication date: 17 March 1998

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

Full work available at URL: https://doi.org/10.1006/jath.1996.3082

zbMATH Keywords

algorithms for obtaining a best approximation elementbest approximation in Hilbert spacesgeometry of convex sets in Hilbert spaces

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Geometry and structure of normed linear spaces (46B20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items

Linear regularity and linear convergence of projection-based methods for solving convex feasibility problems, Best approximation and perturbation property in Hilbert spaces, On basic constraint qualifications for infinite system of convex Inequalities in Banach spaces, Linear regularity and \(\phi\)-regularity of nonconvex sets, Lagrange multiplier characterizations of constrained best approximation with nonsmooth nonconvex constraints, Tangential extremal principles for finite and infinite systems of sets. II: Applications to semi-infinite and multiobjective optimization, Set regularities and feasibility problems, Characterizing nonconvex constrained best approximation using Robinson's constraint qualification, Best approximation with geometric constraints, Lagrange multiplier characterizations of robust best approximations under constraint data uncertainty, Fenchel duality in infinite-dimensional setting and its applications., Moreau--Rockafellar-Type Formulas for the Subdifferential of the Supremum Function, Strong CHIP for infinite systems of convex sets in normed linear spaces, A new projection method for finding the closest point in the intersection of convex sets, Strong Abadie CQ, ACQ, calmness and linear regularity, Bounded linear regularity of convex sets in Banach spaces and its applications, A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces., Uniform subsmoothness and linear regularity for a collection of infinitely many closed sets, Convergence rate of Newton's method for \(L_2\) spectral estimation, Robust constrained best approximation with nonconvex constraints, Reconstruction of functions from prescribed proximal points, Strong CHIP, normality, and linear regularity of convex sets, A Global Approach to Nonlinearly Constrained Best Approximation, Lagrange multiplier characterizations of constrained best approximation with infinite constraints, Fenchel duality and the strong conical hull intersection property, Regularized gap function as penalty term for constrained minimization problems, Best Approximation in a Class of Normed Spaces with Star-Shaped Cone, Normal property, Jameson property, CHIP and linear regularity for an infinite system of convex sets in Banach spaces, Limiting \(\varepsilon\)-subgradient characterizations of constrained best approximation, Strong uniqueness of the restricted Chebyshev center with respect to an RS-set in a Banach space, On best restricted range approximation in continuous complex-valued function spaces, Duality for optimization and best approximation over finite intersections

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Metric regularity, tangent sets, and second-order optimality conditions
• Constrained \(L_ p\) approximation
• Constrained best approximation in Hilbert space. II
• Gauss-Seidel method for least-distance problems
• Best interpolation with convex constraints
• Constrained best approximation in Hilbert space
• Linearly convergent descent methods for the unconstrained minimization of convex quadratic splines
• Constrained best approximation in Hilbert space III. Applications of \(n\)-convex functions
• A nonlinear equation for linear programming
• Smoothing and Interpolation in a Convex Subset of a Hilbert Space
• Regularity and Stability for Convex Multivalued Functions
• A New Algorithm for Solving Strictly Convex Quadratic Programs