# Rapid heuristic projection on simplicial cones

@article{Ekrt2010RapidHP, title={Rapid heuristic projection on simplicial cones}, author={Anik{\'o} Ek{\'a}rt and A. B. N{\'e}meth and S{\'a}ndor Zolt{\'a}n N{\'e}meth}, journal={arXiv: Optimization and Control}, year={2010} }

A very fast heuristic iterative method of projection on simplicial cones is presented. It consists in solving two linear systems at each step of the iteration. The extensive experiments indicate that the method furnishes the exact solution in more then 99.7 percent of the cases. The average number of steps is 5.67 (we have not found any examples which required more than 13 steps) and the relative number of steps with respect to the dimension decreases dramatically. Roughly speaking, for high…

## 8 Citations

### An algorithm for projecting onto simplicial cones

- Mathematics, Computer Science
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A simple and efficient new algorithm for the projection of a given vector in a Euclidean space onto the simplicial cone generated by a set of linearly independent vectors is introduced and compared to other algorithms proposed in the literature.

### Projection onto simplicial cones by a semi-smooth Newton method

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Using Moreau’s decomposition theorem for projecting onto closed convex cones, the problem of projecting onto a simplicial cone is reduced to finding the unique solution of a nonsmooth system of equations.

### Orthogonal projection algorithm for projecting onto a finitely generated cone ∗

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The proposed algorithm to find the nearest point of a convex cone to a given vector, which is composed of a series of orthogonal projections, is proposed and is more stable than other related algorithms.

### A semi-smooth Newton method for solving convex quadratic programming problem under simplicial cone constraint

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In this paper the simplicial cone constrained convex quadratic programming problem is studied. The optimality conditions of this problem consist in a linear complementarity problem. This fact, under…

### On the Projection onto a Finitely Generated Cone

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It is shown that this map is made up of finitely manylinear parts with a structure resembling the facial structure of the finitely generated cone and an economical regarding storage algorithm is presented for calculating the projection of a fixed vector based on Lemke's algorithm to solve a linear complementarity problem.

### A semi-smooth Newton method for a special piecewise linear system with application to positively constrained convex quadratic programming

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### Replacing projection on finitely generated convex cones with projection on bounded polytopes.

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The specialized finite algorithm implemented in the open-source system for matrix-vector calculations octave significantly outperformed a general-purpose quadratic programming algorithm of the active-set variety built into octave when the number of points exceeds the dimensionality of the original problem.

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