We characterize the open sets in the sphere that are geodesically convex in any containing domain with respect to various conformal metrics.

Convexity theory and duality theory are important issues in math- ematical programming. Within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. Furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. Finally,...

This brief is concerned with the $H^{2}$ and notation="LaTeX">$H^{\infty }$ norm-constrained optimization problems of dynamic buffer networks. The extended network model introduced first, wherein weights all edges can be tuned indepen...

We study the relations between boundaries for algebras of holomorphic functions on Banach spaces and complex convexity of their balls. In addition, we show that the Shilov boundary for algebras of holomorphic functions on an order continuous sequence space X is the unit sphere SX if X is locally c-convex. In particular, it is shown that the unit sphere of the OrliczLorentz sequence space λφ,w i...

The Radon number of a graph is the minimum integer r such that all sets of at least r vertices of the graph can be partitioned into two subsets whose convex hulls intersect. We present a near-linear O(d log d) time algorithm to calculate the Radon number of d-dimensional grids in the geodetic convexity. To date, no polynomial time algorithm was known for this problem.

We prove that, at every positive temperature, the infinite-volume free energy of one-dimensional log-gas, or beta-ensemble, has a unique minimizer, which is Sine-beta process arising from random matrix theory. rely on quantitative displacement convexity argument level point processes, and screening procedure introduced by Sandier-Serfaty. © 2021 The Authors. Communications Pure Applied Mathemat...

In this paper we derive some general conditions in order to prove the Schurconvexity of a class of symmetric functions. The log-convexity conditions which appear in this paper will contradicts one of the results of K. Guan from [2]. Also, we prove that a special class of rational maps are Schur-convex functions in Rn +. As an application, Ky-Fan’s inequality is generalized. 2010 Mathematics Sub...

We introduce a new barrier function which is not a barrier function in the usual sense: it has finite value at the boundary of the feasible region. Despite this, its iteration bound, O (√ n logn log n ε ) , is as good as it can be: it is the best known bound for large-update methods. The recently introduced notions of superconvexity and exponential convexity are crucial in the analysis.

We prove the convexity of the negative likelihood function in the asymptotic sense for GARCH models. This property provides assurance for the convergence of numerical optimization algorithms for maximum likelihood estimation of GARCH.A simulation study is conducted in order to compare the performance of several different iteration algorithms. An example based on the log-returns of foreign excha...