Related papers: Order Isomorphisms on Convex Functions in Windows

The concept of convex compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in…

In this paper, one new classes of convex functions which is called MT-convex functions are given. We also establish some Hadamard-type inequalities.

There exist two major subclasses in the class of superquadratic functions, one comprises concave and decreasing functions, while the other consists of convex and monotone increasing functions. Leveraging this distinction, we introduce…

The present paper is concerned with Lipschitz properties of convex mappings. One considers the general context of mappings defined on an open convex subset $\Omega$ of a locally convex space $X$ and taking values in a locally convex space…

We analyze worst-case convergence guarantees of first-order optimization methods over a function class extending that of smooth and convex functions. This class contains convex functions that admit a simple quadratic upper bound. Its study…

We show that minimizing a convex function over the integer points of a bounded convex set is polynomial in fixed dimension.

We identity the optimal non-infinitesimal direction of descent for a convex function. An algorithm is developed that can theoretically minimize a subset of (non-convex) functions.

A unified construction of high order shape functions is given for all four classical energy spaces ($H^1$, $H(\mathrm{curl})$, $H(\mathrm{div})$ and $L^2$) and for elements of "all" shapes (segment, quadrilateral, triangle, hexahedron,…

We study the map associating the cohomology class of an admissible normal function on the product of punctured disks, and give some sufficient conditions for the surjectivity of the map. We also construct some examples such that the map is…

In this paper, we study the family ${\mathcal C}_{H}^0$ of sense-preserving complex-valued harmonic functions $f$ that are normalized close-to-convex functions on the open unit disk $\mathbb{D}$ with $f_{\bar{z}}(0)=0$. We derive a…

Any solid object can be decomposed into a collection of convex polytopes (in short, convexes). When a small number of convexes are used, such a decomposition can be thought of as a piece-wise approximation of the geometry. This…

In this paper, we give some definitions on quasi-convex functions and we prove inequalities contain J-quasi-convex and W-quasi-convex functions. We give also some inclusions.

In this paper, we introduce operator geodesically convex and operator convex-log functions and characterize some properties of them. Then apply these classes of functions to present several operator Azc\'{e}l and Minkowski type inequalities…

The aim of this paper is to give two complete and simple characterizations of Minkowski norms N on an arbitrary topological real vector space such that the sublevel sets of N are strictly convex. We first show that this property is…

We define w-invex set, w-preinvex, w-strictly preinvex, w-quasi preinvex, w-strictly quasi preinvex, w-semi-strictly quasi preinvex, and w-pre pseudo-invex functions in this context. And these form a class of real functions, which is the…

We study various convex functions on $R^n$ associated with positive definite matrices. This yiels some exotic Holder matrix inequalities.

The goal of this paper is to present a complete characterisation of points of order continuity in abstract Ces\`aro function spaces $CX$ for $X$ being a symmetric function space. Under some additional assumptions mentioned result takes the…

A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…

We study the optimization of (strongly) quasar-convex functions, a class that arises naturally in many machine learning and data science applications due to its favorable properties. The fundamental properties of this class are first…

It has been well established that first order optimization methods can converge to the maximal objective value of concave functions and provide constant factor approximation guarantees for (non-convex/non-concave) continuous submodular…