一個閉凸集上的凸函數之研究

The Study on Convex Functions in a Closed Convex Set

黃偉(Huang Wei)

指導教授 ： 張毓麟

國立臺灣師範大學/理學院/數學系/碩士(2016年)

https://doi.org/10.6345/NTNU202204540

摘要

無中文摘要

關鍵字

凸 ； 最佳化 ； 圓錐 ； 跡函數 ； 半正定

並列摘要

We extend to a problem of two-variable function from a monotone condition for the convexity of trace function associated with circular cone in this paper. This structure was based on the Schur Complement Theorem. By smoothing the problem, the greatest benefit is spared the solving time and we believe this establishment will useful in many fields.

並列關鍵字

Convexity ； Optimization ； Circular Cone ； Trace Function ； Positive Semi-definiteness

參考文獻

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[2] J.-S. Chen, T.-K Liao and S.-H. Pan Using Schur Complement Theorem to prove convexity of some SOC-functions, Journal of Nonlinear and Convex Analysis, vol. 13, no. 3, pp. 421-431, 2012.

[3] Jinchuan Zhou, J.-S. Chen and H.-F. Hung Circular cone convexity and some inequalities associated with circular cones, Journal of Inequalities and Applications, 2013:571, 2013.

[4] Jinchuan Zhou and J.-S. Chen, Properties of circular cone and spectral factorization associated with circular cone, Journal of Nonlinear and Convex Analysis, vol. 14, no. 4, pp. 807-816, 2013.

[5] C.-Y. Yang, Y.-L. Chang and J.-S. Chen, Analysis of nonsmooth vector-valued functions associated with infinite-dimensional second-order cones, Nonlinear Analysis: Theory, Methods and Applications, vol. 74, no. 16, pp. 5766-5783, 2011.