تقرير
Directed Discrete Midpoint Convexity
| العنوان: | Directed Discrete Midpoint Convexity |
|---|---|
| المؤلفون: | Tamura, Akihisa, Tsurumi, Kazuya |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, 52A41, 90C27, 90C25 |
| الوصف: | For continuous functions, midpoint convexity characterizes convex functions. By considering discrete versions of midpoint convexity, several types of discrete convexities of functions, including integral convexity, L$^\natural$-convexity and global/local discrete midpoint convexity, have been studied. We propose a new type of discrete midpoint convexity that lies between L$^\natural$-convexity and integral convexity and is independent of global/local discrete midpoint convexity. The new convexity, named DDM-convexity, has nice properties satisfied by L$^\natural$-convexity and global/local discrete midpoint convexity. DDM-convex functions are stable under scaling, satisfy the so-called parallelgram inequality and a proximity theorem with the same small proximity bound as that for L$^{\natural}$-convex functions. Several characterizations of DDM-convexity are given and algorithms for DDM-convex function minimization are developed. We also propose DDM-convexity in continuous variables and give proximity theorems on these functions. Comment: 35 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2001.11676 |
| رقم الأكسشن: | edsarx.2001.11676 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |