On alternative theorems and necessary conditions for efficiency

In this paper, we establish theorems of the alternative for a system described by inequalities, equalities and an inclusion, which are generalizations of Tucker's classical theorem of the alternative, and develop Kuhn-Tucker necessary conditions for efficiency to mathematical programs in normed spaces involving inequality, equality and set constraints with positive Lagrange multipliers of all the components of objective functions.Theorem of the alternative, Kuhn-Tucker necessary condition, constraint qualification.

ON NECESSARY CONDITIONS FOR EFFICIENCY IN DIRECTIONALLY DIFFERENTIABLE OPTIMIZATION PROBLEMS

This paper deals with multiobjective programming problems with in- equality, equality and set constraints involving Dini or Hadamard differentiable func- tions. A theorem of the alternative of Tucker type is established, and from which Kuhn-Tucker necessary conditions for local Pareto minima with positive Lagrange multipliers associated with all the components of objective functions are derived.Theorem of the alternative, Kuhn-Tucker necessary conditions, direc- tionally differentiable functions.

On constraint qualifications with generalized convexity and optimality conditions

This paper deals with a multiobjective programming problem involving both equality constraints in infinite dimensional spaces. It is shown that some constraint qualifications together with a condition of interior points are sufficient conditions for the invexity of constraint maps with respect to the same scale map. Under a new constraint qualification which involves an invexity condition and a generalized Slater condition a Kuhn-Tucker necessary condition is established.Invexity, scale, constraint qualification, nearly S-convelike mapping.

Enabling non-linear energy harvesting in power domain based multiple access in relaying networks: Outage and ergodic capacity performance analysis

The Power Domain-based Multiple Access (PDMA) scheme is considered as one kind of Non-Orthogonal Multiple Access (NOMA) in green communications and can support energy-limited devices by employing wireless power transfer. Such a technique is known as a lifetime-expanding solution for operations in future access policy, especially in the deployment of power-constrained relays for a three-node dual-hop system. In particular, PDMA and energy harvesting are considered as two communication concepts, which are jointly investigated in this paper. However, the dual-hop relaying network system is a popular model assuming an ideal linear energy harvesting circuit, as in recent works, while the practical system situation motivates us to concentrate on another protocol, namely non-linear energy harvesting. As important results, a closed-form formula of outage probability and ergodic capacity is studied under a practical non-linear energy harvesting model. To explore the optimal system performance in terms of outage probability and ergodic capacity, several main parameters including the energy harvesting coefficients, position allocation of each node, power allocation factors, and transmit signal-to-noise ratio (SNR) are jointly considered. To provide insights into the performance, the approximate expressions for the ergodic capacity are given. By matching analytical and Monte Carlo simulations, the correctness of this framework can be examined. With the observation of the simulation results, the figures also show that the performance of energy harvesting-aware PDMA systems under the proposed model can satisfy the requirements in real PDMA applications.Web of Science87art. no. 81

Improving performance of far users in cognitive radio: Exploiting NOMA and wireless power transfer

In this paper, we examine non-orthogonal multiple access (NOMA) and relay selection strategy to benefit extra advantage from traditional cognitive radio (CR) relaying systems. The most important requirement to prolong lifetime of such network is employing energy harvesting in the relay to address network with limited power constraint. In particular, we study such energy harvesting CR-NOMA using amplify-and-forward (AF) scheme to improve performance far NOMA users. To further address such problem, two schemes are investigated in term of number of selected relays. To further examine system performance, the outage performance needs to be studied for such wireless powered CR-NOMA network over Rayleigh channels. The accurate expressions for the outage probability are derived to perform outage comparison of primary network and secondary network. The analytical results show clearly that position of these nodes, transmit signal to noise ratio (SNR) and power allocation coefficients result in varying outage performance. As main observation, performance gap between primary and secondary destination is decided by both power allocation factors and selection mode of single relay or multiple relays. Numerical studies were conducted to verify our derivations.Web of Science1211art. no. 220