An inertial Douglas–Rachford splitting algorithm for nonconvex and nonsmooth problems

AbstractIn this paper, we consider a cognitive radio network scenario, where two primary users want to exchange information with each other and meanwhile, one secondary node wishes to send messages to a cognitive base station. To meet the target quality of service (QoS) of the primary users and raise the communication opportunity of the secondary nodes, a cognitive bidirectional relaying (BDR) scheme is examined. First, system outage probabilities of conventional direct transmission and BDR schemes are presented. Next, a new system parameter called operating region is defined and calculated, which indicates in which position a secondary node can be a cognitive relay to assist the primary users. Then, a cognitive BDR scheme is proposed, giving a transmission protocol along with a time-slot splitting algorithm between the primary and secondary transmissions. Information-theoretic metric of ergodic capacity is studied for the cognitive BDR scheme to evaluate its performance. Simulation results show that with the proposed scheme, the target QoS of the primary users can be guaranteed, while increasing the communication opportunity for the secondary nodes.

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Theory of Boundary Eigensolutions in Engineering Mechanics

Journal of Applied Mechanics ◽

10.1115/1.1331059 ◽

2000 ◽

Vol 68 (1) ◽

pp. 101-108 ◽

Cited By ~ 12

Author(s):

A. R. Hadjesfandiari ◽

G. F. Dargush

Keyword(s):

Weight Function ◽

Mixed Boundary ◽

Traditional Approach ◽

Mixed Boundary Conditions ◽

Boundary Element Methods ◽

Positive Weight ◽

Nonsmooth Problems ◽

Integral Equation Methods ◽

Potential Problems ◽

Engineering Mechanics

A theory of boundary eigensolutions is presented for boundary value problems in engineering mechanics. While the theory is quite general, the presentation here is restricted to potential problems. Contrary to the traditional approach, the eigenproblem is formed by inserting the eigenparameter, along with a positive weight function, into the boundary condition. The resulting spectra are real and the eigenfunctions are mutually orthogonal on the boundary, thus providing a basis for solutions. The weight function permits effective treatment of nonsmooth problems associated with cracks, notches and mixed boundary conditions. Several ideas related to the convergence characteristics are also introduced. Furthermore, the connection is made to integral equation methods and variational methods. This paves the way toward the development of new computational formulations for finite element and boundary element methods. Two numerical examples are included to illustrate the applicability.

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A multi-level splitting algorithm based on differential evolution

International Journal of Modeling Simulation and Scientific Computing ◽

10.1142/s1793962318500216 ◽

2018 ◽

Vol 09 (02) ◽

pp. 1850021

Author(s):

Liping Wang ◽

Wenhui Fan

Keyword(s):

Differential Evolution ◽

Rare Event ◽

Sampling Strategy ◽

Splitting Algorithm ◽

Algorithm Efficiency ◽

Event Simulation ◽

Sample Paths ◽

Level Splitting ◽

Key Factor ◽

Multi Level

Multi-level splitting algorithm is a famous rare event simulation (RES) method which reaches rare set through splitting samples during simulation. Since choosing sample paths is a key factor of the method, this paper embeds differential evolution in multi-level splitting mechanism to improve the sampling strategy and precision, so as to improve the algorithm efficiency. Examples of rare event probability estimation demonstrate that the new proposed algorithm performs well in convergence rate and precision for a set of benchmark cases.

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