Projecting onto intersections of halfspaces and hyperplanes
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Publication:6342740
arXiv2006.06995MaRDI QIDQ6342740
Publication date: 12 June 2020
Abstract: It is well-known that the sequence of iterations of the composition of projections onto closed affine subspaces converges linearly to the projection onto the intersection of the affine subspaces when the sum of the corresponding linear subspaces is closed. Inspired by this, in this work, we systematically study the relation between the projection onto intersection of halfspaces and hyperplanes, and the composition of projections onto halfspaces and hyperplanes. In addition, as by-products, we provide the Karush-Kuhn-Tucker conditions for characterizing the optimal solution of convex optimization with finitely many equality and inequality constraints in Hilbert spaces and construct an explicit formula for the projection onto the intersection of hyperplane and halfspace.
Numerical mathematical programming methods (65K05) Convex programming (90C25) Applications of mathematical programming (90C90) Numerical optimization and variational techniques (65K10) Best approximation, Chebyshev systems (41A50) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10)
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