Related papers: Improved Jensen-type inequalities via linear inter…
Since its original formulation, Jensen's inequality has played a fundamental role across mathematics, statistics, and machine learning, with its probabilistic version highlighting the nonnegativity of the so-called Jensen's gap, i.e., the…
In this paper, we obtain some new inequalities for ({\alpha},m)-convex functions. The analysis used in the proofs is fairly elementary and based on the use of Power-mean inequality.
We extend Carleson's interpolation Theorem to sequences of matrices, by giving necessary and sufficient separation conditions for a sequence of matrices to be interpolating.
A generalization of Mercer inequality for h-convex function is presented. As application, a weighted generalization of triangle inequality is given.
In this paper, we address the problem of interpolation of smooth convex-concave functions. Interpolation is a key step for computer-assisted estimation of worst-case performance via PEP-like techniques, and smooth convex-concave functions…
In this paper a novel hybrid approach for compensating the distortion of any interpolation has been proposed. In this hybrid method, a modular approach was incorporated in an iterative fashion. By using this approach we can get drastic…
The connection formula for the Jackson integral of type $BC_n$ is obtained in the form of a Sears--Slater type expansion of a bilateral multiple basic hypergeometric series as a linear combination of several specific bilateral multiple…
This paper proposes a novel proximal difference-of-convex (DC) algorithm enhanced with extrapolation and aggressive non-monotone line search for solving non-convex optimization problems. We introduce an adaptive conservative update strategy…
The Leja method is a polynomial interpolation procedure that can be used to compute matrix functions. In particular, computing the action of the matrix exponential on a given vector is a typical application. This quantity is required, e.g.,…
This paper is devoted to a generalization of a Hadamard type inequality for the permanent of a complex square matrix. Our proof is based on a non-trivial extension of a technique used in Carlen, Lieb and Loss (Methods and Applications of…
This paper deals with the solving of variational inequality problem where the constrained set is given as the intersection of a number of fixed-point sets. To this end, we present an extrapolated sequential constraint method. At each…
Data is commonly stored in tabular format. Several fields of research are prone to small imbalanced tabular data. Supervised Machine Learning on such data is often difficult due to class imbalance. Synthetic data generation, i.e.,…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
We provide a unified framework that applies to a general family of convex losses across binary and multiclass settings in the overparameterized regime to approximately characterize the implicit bias of gradient descent in closed form.…
In this paper we propose a method for proving some exponential inequalities based on power series expansion and analysis of derivations of the corresponding functions. Our approach provides a simple proof and generates a new class of…
We extend Prekopa's Theorem and the Brunn-Minkowski Theorem from convexity to $F$-subharmonicity. We apply this to the interpolation problem of convex functions and convex sets introducing a new notion of "harmonic interpolation" that we…
In this paper we obtain quite general and definitive forms for Hardy-Littlewood type inequalities. Moreover, when restricted to the original particular cases, our approach provides much simpler and straightforward proofs and we are able to…
Based on the joint bidiagonalization process of a large matrix pair $\{A,L\}$, we propose and develop an iterative regularization algorithm for the large scale linear discrete ill-posed problems in general-form regularization: $\min\|Lx\| \…
The aim of this paper is to prove an improved version of the bounded differences inequality for matrix valued functions, by developing the methods of Mackey et al.: "Matrix Concentration Inequalities via the Method of Exchangeable Pairs".…
In this article, we present exponential-type inequalities for positive linear mappings and Hilbert space operators, by means of convexity and the Mond-Pe\v cari\'c method. The obtained results refine and generalize some known results. As an…