We consider generalized semi-infinite programming problems in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be convex. Considering a lower level constraint qualification, we derive a formula for estimating the subdifferential of the value function. Finally, we establish the Fritz-John necessary optimality con...

The aim of this paper is to establish some new Hermite–Hadamard type inequalities for harmonic h-convex functions involving hypergeometric functions. We also discuss some new and known special cases, which can be deduced from our results. The ideas and techniques of this paper may inspire further research in this field. In recent years, much attention have been given to theory of convexity beca...

Let K(α), 0≤α< 1, denote the class of functions g(z)= z+∑∞n=2anzn which are regular and univalently convex of order α in the unit disc U . Pursuing the problem initiated by Robinson in the present paper, among other things, we prove that if f is regular in U , f(0) = 0, and f(z)+zf ′(z) < g(z)+zg′(z) in U , then (i) f(z) < g(z) at least in |z| < r0, r0 = √ 5/3 = 0.745 . . . if f ∈ K; and (ii) f...

* Presented to the Society, April 7, 1934; received by the editors June 7, 1934. t Subharmonic functions and minimal surfaces, these Transactions, vol. 35 (1933), pp. 648661. Subharmonic functions and surfaces of negative curvature, these Transactions, vol. 35 (1933), pp. 662-674. % See F. Riesz, Sur les fonctions subharmoniques etc., in two parts, Acta Mathematica, vol. 48 1926), pp. 329-343, ...

The concept of Support Vector Regression is extended to a more general class of convex cost functions. It is shown how the resulting convex constrained optimization problems can be eeciently solved by a Primal{Dual Interior Point path following method. Both computational feasibility and improvement of estimation is demonstrated in the experiments.