The paper investigates the problem of maximizing expected sum throughput in a fading multiple access cognitive radio network when secondary user (SU) transmitters have energy harvesting capability, and perform cooperative spectrum sensing. We formulate the problem as maximization of sumcapacity of the cognitive multiple access network over a finite time horizon subject to a time averaged interf...

We are concerned with dynamic optimization processes from a viewpoint of Golden optimality. A path is called Golden if any state moves to the next state repeating the same Golden section in each transition. A policy is called Golden if it, together with a relevant dynamics, yields a Golden path. The probelm is whether an optimal path/policy is Golden or not. This paper minimizes a quadratic cri...

In this paper we put forward an easy-to-implement methodology for solving deterministic or stochastic dynamic programming problems within a standard optimization package such as GAMS. We’ve found the use of orthogonal polynomials to be especially helpful in implementing approximation methods for iterative computation of the infinite-horizon value function, due to their superior convergence prop...

We present the solution of a portfolio optimization problem for an economic agent endowed with a stochastic insurable stream, under a liquidity constraint over the time interval [0, T ]. Generally, the existence of labor income complicates the agent’s decisions. Moreover, in the real world the economic agents are restricted in their ability to borrow against their future labor income. We deal w...

We consider the long time dependence for the moments of displacement <|r|(q)> of infinite horizon billiards, given a bounded initial distribution of particles. For a variety of billiard models we find <|r|(q)> approximately t(gamma(q)) (up to factors of ln t). The time exponent, gamma(q), is piecewise linear and equal to q/2 for q<2 and q-1 for q>2. We discuss the lack of dependence of this res...

We consider an economy in which there is an infinite stream of pies, each of size one, one in every period. For each agent, the per-period utility function, which is defined on that period’s consumption, is determined by the previous period’s consumption. We describe specifications of this model for which no symmetric, efficient, and monotonic way to allocate pies exists.

This note studies a general nonstationary infinite-horizon optimization problem in discrete time. We allow the state space in each period to be an arbitrary set, and the return function in each period to be unbounded. We do not require discounting, and do not require the constraint correspondence in each period to be nonempty-valued. The objective function is defined as the limit superior or in...

We perform a systematic study of optimization problems in the Wasserstein spaces that are analogs of infinite horizon, deterministic control problems. We derive necessary conditions on action minimizing paths and present a sufficient condition for their existence. We also verify that the corresponding generalized value functions are a type of viscosity solution of a time independent, Hamilton–J...

Given a sequence [Formula: see text] of measurable functions on a σ-finite measure space such that the integral of each [Formula: see text] as well as that of [Formula: see text] exists in [Formula: see text], we provide a sufficient condition for the following inequality to hold: [Formula: see text] Our condition is considerably weaker than sufficient conditions known in the literature such as...