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AN OPTIMAL CONTROL APPROACH TO CONFORMAL FLATTENING OF TRIANGULATED SURFACES
박예솜,이병준,민조홍 한국산업응용수학회 2019 Journal of the Korean Society for Industrial and A Vol.23 No.4
This article presents a new approach for conformal flattening with optimal cone singularity. The algorithm here takes an optimal control for selecting optimal cones and uses the Ricci flow to force the flattening. This work is considered as a modification to the work of Soliman et al. [1] in the sense that they make use of the Yamabe equation for the flatten-ing, which is an approximation of the Ricci flow. We present a numerical algorithm based on the optimal control with the mathematical background. Several numerical results validate that our method is optimal in total cone angle and usage of the Ricci flow ensures the conformal flattening while selecting optimal cones.
AN OPTIMAL BOOSTING ALGORITHM BASED ON NONLINEAR CONJUGATE GRADIENT METHOD
JOOYEON CHOI,BORA JEONG,박예솜,JIWON SEO,민조홍 한국산업응용수학회 2018 Journal of the Korean Society for Industrial and A Vol.22 No.1
Boosting, one of the most successful algorithms for supervised learning, searches the most accurate weighted sum of weak classifiers. The search corresponds to a convex programming with non-negativity and affine constraint. In this article, we propose a novel Conjugate Gradient algorithm with the Modified Polak-Ribiera-Polyak conjugate direction. The convergence of the algorithm is proved and we report its successful applications to boosting.