关于凸性相对于费用函数的结构性结果
Structural results on convexity relative to cost functions
摘要：
大量的运输问题出现在数学的各个领域，其解决方案涉及成本凸势。Fenchel对偶也代表了一个重要的概念，为各种各样的最优化问题，无论是从理论和计算的观点。通过研究代价凸性及其与通常凸性的联系，我们与经典的凸函数理论进行了比较。给出了代价凸函数的Jensen不等式的一个推广.
英文摘要：
Mass transportation problems appear in various areas of mathematics, their solutions involving cost convex potentials. Fenchel duality also represents an important concept for a wide variety of optimization problems, both from the theoretical and the computational viewpoints. We drew a parallel to the classical theory of convex functions by investigating the cost convexity and its connections with the usual convexity. We give a generalization of Jensen's inequality for cost convex functions.
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