The context for this paper is Feferman’s theory of explicit mathematics, a formal framework serving many purposes. It is suitable for representing Bishop-style constructive mathematics as well as generalized recursion, including direct expression of structural concepts which admit self-application. The object of investigation here is the theory of explicit mathematics augmented by the monotone ...

We consider a generalized proximal point method (GPPA) for solving the nonlinear complementarity problem with monotone operators in R ' \ lt differs from the classical proximal point method discussed by Rockafellar for the problem offinding zeroes of monotone operators in the use of generalized distances, called (p-divergences, instead of the Euclidean one. These distances play not only a regul...

In this paper we derive a lattice model with infinite distributed delay to describe the growth of a single-species population in a 2D patchy environment with infinite number of patches connected locally by diffusion and global interaction. We consider the existence of traveling wave solutions when the birth rate is large enough that each patch can sustain a positive equilibrium. When the birth ...

In this paper, we propose a fully polynomial-time randomized approximation scheme (FPRAS) for the closed Jackson network. Our algorithm is based on Markov chain Monte Carlo (MCMC) method. Thus, our scheme returns an approximate solution, of which the size of error satisfies a given error rate. To our knowledge, the algorithm is the first polynomial time MCMC algorithm for closed Jackson network...

We consider the problem of Data Flow Analysis over monotone data flow frameworks with a finite lattice. The problem of computing the Maximum Fixed Point (MFP) solution is shown to be P-complete even when the lattice has just four elements. This shows that the problem is unlikely to be efficiently parallelizable. It is also shown that the problem of computing the Meet Over all Paths (MOP) soluti...

A fundamental result due to Rockafellar states that every cyclically monotone operatorA admits an antiderivative f in the sense that the graph ofA is contained in the graph of the subdifferential operator ∂f . Given a method m that assigns every finite cyclically monotone operator A some antiderivative mA, we say that the method is primal-dual symmetric if m applied to the inverse of A produces...

In this paper, a novel generalized value iteration technique is presented for solving online the discounted linear quadratic (LQ) optimal control problems for continuous-time (CT) linear systems with an unknown system matrix A. In the proposed method, the discounted value function is considered, which is a general setting in reinforcement learning (RL) frameworks, but not fully considered in RL...

is not properly contained in the graph of any other monotone mapping. It is known that T is maximal iff R(I+rT ) = H for every r > 0, where R(I+rT ) = ∪ {z+rTz : z ∈ H,Tz ̸= ∅}. Monotone operators have proven to be a key class of objects in modern Optimization and Analysis; see, e.g., the books [1-7] and the references therein. Let us consider the zero point problem for a monotone operator T on ...

An important and perhaps interesting topic in nonlinear analysis and convex optimization concerns solving inclusions of the form 0 ∈ A(x), where A is a maximal monotone operator on a Hilbert space H. Its importance in convex optimization is evidenced from the fact that many problems that involve convexity can be formulated as finding zeros of maximal monotone operators. For example, convex mini...

Numerical solutions of 2× 2 semilinear systems of elliptic boundary value problems, whose nonlinearities are of quasimonotone nondecreasing, quasimonotone nonincreasing, or mixed quasimonotone types, are computed. At each step of the (quasi) monotone iteration, the solution is represented by a simple-layer potential plus a domain integral; the simple-layer density is then discretized by boundar...