Abstract. We consider the problem of minimizing the sum of a convex function and of p > 1 fractions subject to convex constraints. The numerators of the fractions are positive convex functions, and the denominators are positive concave functions. Thus, each fraction is quasi-convex. We give a brief discussion of the problem and prove that in spite of its special structure, the problem is NPcomp...

This paper introduces and analyses a new algorithm for minimizing a convex function subject to a finite number of convex inequality constraints. It is assumed that the Lagrangian of the problem is strongly convex. The algorithm combines interior point methods for dealing with the inequality constraints and quasi-Newton techniques for accelerating the convergence. Feasibility of the iterates is ...

‎In this paper‎, ‎first we study the weak and strong convergence of solutions to the‎ ‎following first order nonhomogeneous gradient system‎ ‎$$begin{cases}-x'(t)=nablaphi(x(t))+f(t), text{a.e. on} (0,infty)\‎‎x(0)=x_0in Hend{cases}$$ to a critical point of $phi$‎, ‎where‎ ‎$phi$ is a $C^1$ quasi-convex function on a real Hilbert space‎ ‎$H$ with ${rm Argmin}phineqvarnothing$ and $fin L^1(0...

The purpose of this paper is to use the modified block iterative method to propose an algorithm for solving the convex feasibility problems for an infinite family of quasi-φ-asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces with Kadec-Klee property. The results presented in the p...

This paper addresses the long-time behaviour of gradient flows of non convex functionals in Hilbert spaces. Exploiting the notion of generalized semiflows by J. M. Ball, we provide some sufficient conditions for the existence of a global attractor. The abstract results are applied to various classes of non convex evolution problems. In particular, we discuss the longtime behaviour of solutions ...

Assume there exists a quasi-one-to-one, measurable and simply irreducible totally integral function. It has long been known that there exists a quasi-partially covariant contra-smoothly singular, Lindemann, totally irreducible point [19]. We show that there exists a Kovalevskaya and invariant convex algebra. We wish to extend the results of [19] to extrinsic, contravariant, Lambert curves. It w...

Some new concepts of generating spaces of quasi-norm family are introduced and their linear topological structures are studied. These spaces are not necessarily locally convex. By virtue of some properties in these spaces, several Schauder-type fixed point theorems are proved, which include the corresponding theorems in locally convex spaces as their special cases. As applications, some new fix...

The problem of L1-convergence of the Fourier cosine series (1.1) has been settled for various special classes of coefficients. Young [6] found that an logn= o(1), n→∞ is a necessary and sufficient condition for cosine series with convex (∆an ≥ 0) coefficients, and Kolmogorov [5] extended this result to the cosine series with quasi-convex ( ∑∞ n=1n|∆an−1| < ∞) coefficients. Later, Garrett and St...