Adaptive Multi-objective Optimization for Energy Efficient Interference Coordination in Multi-Cell Networks

In this paper, we investigate the distributed power allocation for multi-cell OFDMA networks taking both energy efficiency and inter-cell interference (ICI) mitigation into account. A performance metric termed as throughput contribution is exploited to measure how ICI is effectively coordinated. To achieve a distributed power allocation scheme for each base station (BS), the throughput contribution of each BS to the network is first given based on a pricing mechanism. Different from existing works, a biobjective problem is formulated based on multi-objective optimization theory, which aims at maximizing the throughput contribution of the BS to the network and minimizing its total power consumption at the same time. Using the method of Pascoletti and Serafini scalarization, the relationship between the varying parameters and minimal solutions is revealed. Furthermore, to exploit the relationship an algorithm is proposed based on which all the solutions on the boundary of the efficient set can be achieved by adaptively adjusting the involved parameters. With the obtained solution set, the decision maker has more choices on power allocation schemes in terms of both energy consumption and throughput. Finally, the performance of the algorithm is assessed by the simulation results.Comment: 29 page

Adjoint-based predictor-corrector sequential convex programming for parametric nonlinear optimization

This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that guarantees the tracking performance of the algorithm. Two variants of this algorithm are investigated. The first one can be used to solve nonlinear programming problems while the second variant is aimed to treat online parametric nonlinear programming problems. The local convergence of these variants is proved. An application to a large-scale benchmark problem that originates from nonlinear model predictive control of a hydro power plant is implemented to examine the performance of the algorithms.Comment: This manuscript consists of 25 pages and 7 figure

A phase-field model for fractures in incompressible solids

Within this work, we develop a phase-field description for simulating fractures in incompressible materials. Standard formulations are subject to volume-locking when the solid is (nearly) incompressible. We propose an approach that builds on a mixed form of the displacement equation with two unknowns: a displacement field and a hydro-static pressure variable. Corresponding function spaces have to be chosen properly. On the discrete level, stable Taylor-Hood elements are employed for the displacement-pressure system. Two additional variables describe the phase-field solution and the crack irreversibility constraint. Therefore, the final system contains four variables: displacements, pressure, phase-field, and a Lagrange multiplier. The resulting discrete system is nonlinear and solved monolithically with a Newton-type method. Our proposed model is demonstrated by means of several numerical studies based on two numerical tests. First, different finite element choices are compared in order to investigate the influence of higher-order elements in the proposed settings. Further, numerical results including spatial mesh refinement studies and variations in Poisson's ratio approaching the incompressible limit, are presented