• The dual problem is always convex no matter if the primal problem is convex, i.e., g is always concave. • The primal and dual optimal values, f∗ and g∗, always satisfy weak duality: f∗ ≥ g∗. • Slater’s condition: for convex primal, if there is an x such that h1(x) < 0, · · · , hm(x) < 0 and l1(x) = 0, · · · , lr(x) = 0 (12.5) then strong duality holds: f∗ = g∗. Note that the condition can be ...

The paper presents a framework, in which the main concepts of schema and data integration can be specified both semantically and syntactically in an abstract data-model independent way. We first define what are schema matching and integration semantically, in terms of sets of instances and mappings between them. We also define a schema matching and integration syntactically, and introduce a pro...

let c be a field of subsets of a set i. also, let     1 i i be a non-decreasing positivesequence of real numbers such that 1, 1 0 1   i  and    11 i i . in this paper we prove thatbv of all the games of -bounded variation on c is a non-separable and norm dual banach space of thespace of simple games on c . we use this fact to establish the existence of a linear mapping t from...

Abstract We propose a simple variant of the generalized Frank–Wolfe method for solving strongly convex composite optimization problems, by introducing an additional averaging step on dual variables. show that in this variant, one can choose constant step-size and obtain linear convergence rate duality gaps. By leveraging analysis we then analyze local logistic fictitious play algorithm, which i...

in this paper we nd solution of linear interval equation in dual form based on the generalizedprocedure of interval extension which is called interval extended zero method.moreover, proposed method has signicant advantage, is that it substantially decreasesthe excess width eect.

In this paper, we define new subclass of analytic functions related with bounded positive real part, and coefficients estimates, duality and neighborhood are considered.