A relaxed projection method for variational inequalities
Mathematical Programming: Series A and B
A simultaneous iterative method for computing projections on polyhedra
SIAM Journal on Control and Optimization
A successive projection method
Mathematical Programming: Series A and B
A parallel algorithm for a class of convex programs
SIAM Journal on Control and Optimization
On the convergence of Han's method for convex programming with quadratic objective
Mathematical Programming: Series A and B
Dual coordinate ascent methods for non-strictly convex minimization
Mathematical Programming: Series A and B
Dykstra's alternating projection algorithm for two sets
Journal of Approximation Theory
A row-action method for convex programming
Mathematical Programming: Series A and B
Primal-dual row-action method for convex programming
Journal of Optimization Theory and Applications
Two generalizations of Dykstra's cyclic projections algorithm
Mathematical Programming: Series A and B
Strong Convergence of Block-Iterative Outer Approximation Methods for Convex Optimization
SIAM Journal on Control and Optimization
Mathematics of Operations Research
Optimization by Vector Space Methods
Optimization by Vector Space Methods
Parallel Optimization: Theory, Algorithms and Applications
Parallel Optimization: Theory, Algorithms and Applications
A Weak-to-Strong Convergence Principle for Fejé-Monotone Methods in Hilbert Spaces
Mathematics of Operations Research
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We present a modification of Dykstra's algorithm which allows us to avoid projections onto general convex sets. Instead, we calculate projections onto either a half-space or onto the intersection of two half-spaces. Convergence of the algorithm is established and special choices of the half-spaces are proposed.The option to project onto half-spaces instead of general convex sets makes the algorithm more practical. The fact that the half-spaces are quite general enables us to apply the algorithm in a variety of cases and to generalize a number of known projection algorithms.The problem of projecting a point onto the intersection of closed convex sets receives considerable attention in many areas of mathematics and physics as well as in other fields of science and engineering such as image reconstruction from projections.In this work we propose a new class of algorithms which allow projection onto certain super half-spaces, i.e., half-spaces which contain the convex sets. Each one of the algorithms that we present gives the user freedom to choose the specific super half-space from a family of such half-spaces. Since projecting a point onto a half-space is an easy task to perform, the new algorithms may be more useful in practical situations in which the construction of the super half-spaces themselves is not too difficult.