1 n : (n, f) = 1 0 : otherwise , the absolute convergence for s > 1 follows from the convergence of ζQ(s) for s > 1. (ii) Given the convergence for s > 1, the proof of the product expansion is identical to the case ζQ(s). We also observe that L(s, χ1) = ζQ(s). As we will see, for non-trivial characters, the L-series behave rather differently. We will analyze these functions further, but first w...

Abstract. This paper provides a detailed analysis of a primal-dual interior-point method for PDE-constrained optimization. Considered are optimal control problems with control constraints in L. It is shown that the developed primal-dual interior-point method converges globally and locally superlinearly. Not only the easier L-setting is analyzed, but also a more involved L-analysis, q < ∞, is pr...

In this paper, $(p,q)$-Lupas Bernstein Stancu operators are constructed. Statistical as well as other approximation properties of $(p,q)$-Lupac{s} Stancu operators are studied. Rate of statistical convergence by means of modulus of continuity and Lipschitz type maximal functions has been investigated.

We address two open theoretical questions in Policy Gradient Reinforcement Learning. The first concerns the efficacy of using function approximation to represent the state action value function, Q. Theory is presented showing that linear function approximation representations of Q can degrade the rate of convergence of performance gradient estimates by a factor of O(ML) relative to when no func...

In this paper, we first characterize the convex $L$-subgroup of an $L$-ordered group by means of fourkinds of cut sets of an $L$-subset. Then we consider the homomorphic preimages and the product of convex $L$-subgroups.After that, we introduce an $L$-convex structure constructed by convex $L$-subgroups.Furthermore, the notion of the degree to which an $L$-subset of an $L$-ord...

Bounds for the bracketing entropy of the classes of bounded k-monotone functions on [0, A] are obtained under both the Hellinger distance and the L(p)(Q) distance, where 1 ≤ p < ∞ and Q is a probability measure on [0, A]. The result is then applied to obtain the rate of convergence of the maximum likelihood estimator of a k-monotone density.

In this paper, we introduce and study a generalized Yosida approximation operator associated to H(·, ·)-co-accretive operator and discuss some of its properties. Using the concept of graph convergence and resolvent operator, we establish the convergence for generalized Yosida approximation operator. Also, we show an equivalence between graph convergence for H(·, ·)-co-accretive operator and gen...

We explore the distinction between convergence and absolute convergence of series in both Archimedean and non-Archimedean ordered fields and find that the relationship between them is closely connected to sequential (Cauchy) completeness.

We study the convergence properties of an alternating proximal minimization algorithm for nonconvex structured functions of the type: L(x, y) = f(x)+Q(x, y)+g(y), where f : Rn → R∪{+∞} and g : Rm → R∪{+∞} are proper lower semicontinuous functions, and Q : Rn × Rm → R is a smooth C function which couples the variables x and y. The algorithm can be viewed as a proximal regularization of the usual...