«convex function»
۲۴٬۹۸۰ نتیجهA New Subclass of Close-to-convex Functions
In this work, we introduce and investigate an interesting subclass Xt(γ) of analytic and close-to-convex functions in the open unit disk U. For functions belonging to the class Xt(γ), we drive several properties including coefficient estimates, distortion theorems, covering theor
Adaptive, anisotropic and hierarchical cones of discrete convex functions
We introduce a new class of adaptive methods for optimization problems posed on the cone of convex functions. Among the various mathematical problems which posses such a formulation, the Monopolist problem [24, 10] arising in economics is our main motivation. Consider a two dimen
Solving Indefinite Kernel Support Vector Machine with Difference of Convex Functions Programming
Indefinite kernel support vector machine (IKSVM) has recently attracted increasing attentions in machine learning. Different from traditional SVMs, IKSVM essentially is a non-convex optimization problem. Some algorithms directly change the spectrum of the indefinite kernel matrix
Generic G&eaux- Differentiability of Convex Functions on Small Sets
The theory of generic differentiability of convex functions on Banach spaces is by now a well-explored part of infinite-dimensional geometry. All the attempts to solve this kind of problem have in common, as a working hypothesis, one special feature of the finite-dimensional case
Escaping the Local Minima via Simulated Annealing: Optimization of Approximately Convex Functions
We consider the problem of optimizing an approximately convex function over a bounded convex set in Rn using only function evaluations. The problem is reduced to sampling from an approximately log-concave distribution using the Hit-and-Run method, which is shown to have the same
Accepted for publication in the Transactions of the American Math. Society (1990) GENERALIZED SECOND DERIVATIVES OF CONVEX FUNCTIONS AND SADDLE FUNCTIONS
The theory of second-order epi-derivatives of extended-real-valued functions is applied to convex functions on lR and shown to be closely tied to proto-differentiation of the corresponding subgradient multifunctions, as well as to second-order epi-differentiation of conjugate fun
On the Relations between Two Types of Convergence for Convex Functions
Theory and applications have shown that there are two important types of convergence for convex functions: pointwise convergence and convergence in a topology induced by the convergence of their epigraphs. We show that these two types of convergence are equivalent on the class of
Maximum and Comparison Principles for Convex Functions on the Heisenberg Group
The purpose in this paper is to establish pointwise estimates for a class of convex functions on the Heisenberg group. An integral estimate for classical convex functions in terms of the Monge–Ampère operator det D2u was proved by Aleksandrov, see [3, Theorem 1.4.2]. Such estimat
MATHEMATICAL ENGINEERING TECHNICAL REPORTS On Infimal Convolution of M-Convex Functions
The infimal convolution of M-convex functions is M-convex. This is a fundamental fact in discrete convex analysis that is often useful in its application to mathematical economics and game theory. M-convexity and its variant called M-convexity are closely related to gross substit
A New Class of Convex Functions for Delay Modeling and Its Application to the Transistor Sizing Problem
This paper derives a methodology for developing accurate convex delay models to be used for transistor sizing. A new rich class of convex functions to model gate delay is presented and the circuit delay under such a model is shown to be equivalent to a convex function. The richne