An efficient algorithm for the projection of a point on the intersection of two hyperplanes and a box in $$\mathbb {R}^n$$
Here, we present an efficient strongly polynomial algorithm for the projection of a point on the intersection of two hyperplanes and a box in \(\mathbb {R}^n\). Interior point methods are the most efficient algorithm in the literature to solve this problem. While efficient in practice, the complexity of interior-point methods is bounded by a polynomial in the dimension of the problem and in the accuracy of the solution. Moreover, their efficiency is highly dependent on a series of parameters depending on the specific method chosen (especially for nonlinear problems), such as step size, barrier parameter, accuracy, among others. We propose a new method based on the KKT optimality conditions. In this method, we write the problem as a function of the Lagrangian multipliers of the hyperplanes and seek to find the pair of multipliers that corresponds to the optimal solution. We prove that the algorithm has complexity \(O(n^2 \log n)\).
- Research Organization:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ); USDOE National Nuclear Security Administration (NNSA)
- Grant/Contract Number:
- AC52-07NA27344
- OSTI ID:
- 1756153
- Report Number(s):
- LLNL-JRNL--622612; 730552
- Journal Information:
- EURO Journal on Computational Optimization, Journal Name: EURO Journal on Computational Optimization Journal Issue: 2 Vol. 7; ISSN 2192-4406
- Publisher:
- Springer NatureCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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