We introduce new methods for defining generalized sums of monotone operators and generalized compositions of monotone operators with linear maps. Under asymptotic conditions we show these operations coincide with the usual ones. When the monotone operators are subdifferentials of convex functions, a similar conclusion holds. We compare these generalized operations with previous constructions by...

In this paper, we consider a class of nonsmooth, nonconvex constrained optimization problems where the objective function may be not Lipschitz continuous and the feasible set is a general closed convex set. Using the theory of the generalized directional derivative and the Clarke tangent cone, we derive a first order necessary optimality condition for local minimizers of the problem, and define...

In this paper we address the basic geometric question of when a given convex set is the image under a linear map of an affine slice of a given closed convex cone. Such a representation or “lift” of the convex set is especially useful if the cone admits an efficient algorithm for linear optimization over its affine slices. We show that the existence of a lift of a convex set to a cone is equival...

in this paper, we prove some coupled coincidence point theorems for mappings satisfying generalized contractive conditions under a new invariant set in ordered cone metric spaces. in fact, we obtain sufficient conditions for existence of coupled coincidence points in the setting of cone metric spaces. some examples are provided to verify the effectiveness and applicability of our results.

We analyze the convex combinations of noninvertible generalized Pauli dynamical maps. By manipulating mixing parameters, one can produce a channel with shifted singularities, additional or even no singularities whatsoever. In particular, we show how to use maps Markovian semigroup. Interestingly, whose results in semigroup are generated by time-local generators and time-homogeneous memory kerne...