Distributed Interior-point Method for Loosely Coupled Problems

In this paper, we put forth distributed algorithms for solving loosely coupled unconstrained and constrained optimization problems. Such problems are usually solved using algorithms that are based on a combination of decomposition and first order methods. These algorithms are commonly very slow and require many iterations to converge. In order to alleviate this issue, we propose algorithms that combine the Newton and interior-point methods with proximal splitting methods for solving such problems. Particularly, the algorithm for solving unconstrained loosely coupled problems, is based on Newton's method and utilizes proximal splitting to distribute the computations for calculating the Newton step at each iteration. A combination of this algorithm and the interior-point method is then used to introduce a distributed algorithm for solving constrained loosely coupled problems. We also provide guidelines on how to implement the proposed methods efficiently and briefly discuss the properties of the resulting solutions.Comment: Submitted to the 19th IFAC World Congress 201

Robust Stability Analysis of Sparsely Interconnected Uncertain Systems

In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis of such systems can be performed by solving a set of sparse linear matrix inequalities. We also show that a sparse formulation of the analysis problem is equivalent to the classical formulation of the robustness analysis problem and hence does not introduce any additional conservativeness. The sparse formulation of the analysis problem allows us to apply methods that rely on efficient sparse factorization techniques, and our numerical results illustrate the effectiveness of this approach compared to methods that are based on the standard formulation of the analysis problem.Comment: Provisionally accepted to appear in IEEE Transactions on Automatic Contro

Distributed Robust Stability Analysis of Interconnected Uncertain Systems

This paper considers robust stability analysis of a large network of interconnected uncertain systems. To avoid analyzing the entire network as a single large, lumped system, we model the network interconnections with integral quadratic constraints. This approach yields a sparse linear matrix inequality which can be decomposed into a set of smaller, coupled linear matrix inequalities. This allows us to solve the analysis problem efficiently and in a distributed manner. We also show that the decomposed problem is equivalent to the original robustness analysis problem, and hence our method does not introduce additional conservativeness.Comment: This paper has been accepted for presentation at the 51st IEEE Conference on Decision and Control, Maui, Hawaii, 201

Distributed Robustness Analysis of Interconnected Uncertain Systems Using Chordal Decomposition

Large-scale interconnected uncertain systems commonly have large state and uncertainty dimensions. Aside from the heavy computational cost of solving centralized robust stability analysis techniques, privacy requirements in the network can also introduce further issues. In this paper, we utilize IQC analysis for analyzing large-scale interconnected uncertain systems and we evade these issues by describing a decomposition scheme that is based on the interconnection structure of the system. This scheme is based on the so-called chordal decomposition and does not add any conservativeness to the analysis approach. The decomposed problem can be solved using distributed computational algorithms without the need for a centralized computational unit. We further discuss the merits of the proposed analysis approach using a numerical experiment.Comment: 3 figures. Submitted to the 19th IFAC world congres

Higher education in Lebanon : management cultures and their impact on performance outcomes

This research study takes a close look at the higher education system in Lebanon. It attempts to identify the principal management cultures in seven institutes of higher education each adopting a different educational system – American, French, Egyptian and Lebanese. McNay’s quartet of collegium, bureaucracy, corporation and enterprise was used as a main reference, with positioning on the model determined by the two dimensions of policy definition and control over implementation each defined as either ‘loose’ or ‘tight’. The study describes and analyzes the organisational structures of the institutions in an attempt to determine the characteristics of the power and authority relationships of each culture and the modes of decision-making. The research study further investigates the degree of academic and institutional autonomy, the measures of accountability and the mechanisms of internal and external scrutiny adopted by the institutes. While McNay’s typology serves as a base to begin to categorise the management cultures of these institutes, no neat categorisation emerged from the combination of the various data sources used in the study. Elements of all four cultures exist in all universities, with dominance for features of the bureaucratic and the corporate cultures. Factors such as the degree of secularisation of the institutions and their cultural origins, whether Lebanese, Arab or Western, seem to impact on institutional culture and are manifested in a distinctive personalised mode of management that emphasises control, power and loyalty, which are deep seated cultural traits of the people of Lebanon and the region. In evaluating the changing environment of higher education, student views on ‘quality’ are also important. The study highlights the differences between institutional types in relation to student performance outputs based on students’ perceptions of their overall educational experience such as teaching and learning experiences. Students in all institutions expressed satisfaction with the education they were receiving; however students in American patterned universities seemed to be exposed to a more liberal form.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Exploiting Chordality in Optimization Algorithms for Model Predictive Control

In this chapter we show that chordal structure can be used to devise efficient optimization methods for many common model predictive control problems. The chordal structure is used both for computing search directions efficiently as well as for distributing all the other computations in an interior-point method for solving the problem. The chordal structure can stem both from the sequential nature of the problem as well as from distributed formulations of the problem related to scenario trees or other formulations. The framework enables efficient parallel computations.Comment: arXiv admin note: text overlap with arXiv:1502.0638