TL;DR
This paper discusses climbing algorithms, like the Dual Matrix Algorithm for linear programming, which enable easy assessment of solution proximity and flexibility in solving NP problems, with potential for further development.
Contribution
It introduces climbing algorithms as a flexible approach for linear programming, building on historical algorithms with robustness and adaptability.
Findings
Climbing algorithms allow real-time assessment of solution quality.
DMA is robust to numerical errors and inequality variations.
Potential for further algorithmic developments is highlighted.
Abstract
NP (search) problems allow easy correctness tests for solutions. Climbing algorithms allow also easy assessment of how close to yielding the correct answer is the configuration at any stage of their run. This offers a great flexibility, as how sensible is any deviation from the standard procedures can be instantly assessed. An example is the Dual Matrix Algorithm (DMA) for linear programming, variations of which were considered by A.Y. Levin in 1965 and by Yamnitsky and myself in 1982. It has little sensitivity to numerical errors and to the number of inequalities. It offers substantial flexibility and, thus, potential for further developments.
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