We propose a new framework for black-box convex optimization which is well-suited for situations where gradient computations are expensive. We derive a new method for this framework which leverages several concepts from convex optimization, from standard first-order methods (e.g. gradient descent or quasi-Newton methods) to analytical centers (i.e. minimizers of self-concordant barriers). We de...

be the Fourier cosine series. The problem of L-convergence of the Fourier cosine series (1.1) has been settled for various special classes of coefficients. Young [9] found that an logn = o(1), n → ∞ is a necessary and sufficient condition for the L-convergence of the cosine series with convex (△an ≥ 0) coefficients, and Kolmogorov [8] extended this result to the cosine series with quasi-convex ( ∞

Smooth K-functors are introduced and the smooth K-theory of locally convex algebras is developed. It is proved that the algebraic and smooth K-functors are isomorphic on the category of quasi ⊗̂-stable real (or complex) Fréchet algebras.

In this paper, we consider an iteration process to approximate a common random fixed point of a finite family of asymptotically quasi-nonexpansive random mappings in convex metric spaces. Our results extend and improve several known results in recent literature.

In this paper, we give a unified approach to establish midpoint, trapezoid, and Simpson’s inequalities for functions whose derivatives in absolute value at certain power are quasi-convex. Some applications to special means of real numbers are also given.

In this paper we present some inequalities of Hermite-Hadamard type for functions whose third derivative absolute values are quasi-convex. Moreover, an application to special means of real numbers is also considered.

In this paper we study the Pareto-optimal solutions in convex multi-objective optimization with compact and convex feasible domain. One of the most important problems in multi-objective optimization is the investigation of the topological structure of the Pareto sets. We present the problem of construction of a retraction function of the feasible domain onto Paretooptimal set, if the objective ...

We characterize convex cocompact subgroups of mapping class groups that arise as subgroups of specially embedded right-angled Artin groups. That is, if the right-angled Artin group G < Mod(S) satisfies certain conditions that imply G is quasi-isometrically embedded in Mod(S), then a purely pseudo-Anosov subgroup H < G is convex cocompact in Mod(S) if and only if it is combinatorially quasiconve...

Abstract In this paper, we present the Sugeno integral of Hermite–Hadamard inequality for case quasi-arithmetically convex (q-ac) functions which acts as a generator all quasi-arithmetic means in frame work integral.

It is known that vector variational inequality models arises from vector optimization and vector traac equilibria. In this paper, existence results of a solution for a generalized pre-vector variational inequality and a generalized pre-quasi-vector variational inequality are established. The main condition used is that the underlying vector-valued function is assumed to be cone-quasi-convex. Th...