Finding globally shortest paths through a sequence of adjacent triangles by the method of orienting curves

Phan Thanh An () and Hoang Xuan Phu ()
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Phan Thanh An: Ho Chi Minh City University of Technology (HCMUT)
Hoang Xuan Phu: Vietnam Academy of Science and Technology

Journal of Global Optimization, 2023, vol. 85, issue 4, No 10, 1037-1063

Abstract: Abstract In this paper, an exact algorithm based on the method of orienting curves is developed for solving the convex non-differentiable optimization problem on the closed unit cube in a finite dimensional space: finding the shortest path joining two points going through a sequence of adjacent triangles in 3D. As a result, the global solution of the problem is determined successively by some orienting curves and final curve, which can be exactly constructed with ruler and compass. A detailed numerical example is presented.

Keywords: Convex non-differentiable optimization; Exact algorithm; Global solution; Path planning; Planar unfolding; Polyhedral surface; Polytope; Shortest path; Straightest geodesic; 05C85; 52B55; 52B55; 52B05; 65D19; 65Y10; 68R10; 68W25; 90C59 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01244-x

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