Parallel computing in network optimization

Caption title.Includes bibliographical references (p. 82-95).Supported by the NSF. CCR-9103804Dimitri Bertsekas ... [et al.]

An alternating direction method for linear programming

Cover title.Includes bibliographical references (p. 41-44).Research partially supported by the Army Research Office. DAAL03-86-K-0171 Research partially supported by the National Science Foundation. ECS-8519058by Jonathan Eckstein, Dimitri P. Bertsekas

A BLOCK-PARALLEL CONJUGATE GRADIENT METHOD FOR SEPARABLE QUADRATIC PROGRAMMING PROBLEMS1

Abstract For a large-scale quadratic programming problem with separable objective function, a variant of the conjugate gradient method can effectively be applied to the dual problem. In this paper, we consider a block-parallel modification of the conjugate gradient method, which is suitable for implementation on a parallel computer. More precisely, the method proceeds in a block Jacobi manner and executes the conjugate gradient iteration to solve quadratic programming subproblems associated with respective blocks. We implement the method on a Connection Machine Model CM-5 in the Single-Program Multiple-Data model of computation. We report some numerical results, which show that the proposed method is effective particularly for problems with some block structure

Distribution power markets: detailed modeling and tractable algorithms

The increasing integration of renewable generation presents power systems with economic and reliability challenges, mostly due to renewables' volatility, which cannot be effectively addressed with business-as-usual practices. Fortunately, this is concurrent with rising levels of Distributed Energy Resources (DERs), including photovoltaics, microgeneration and flexible loads like HVAC loads and electric vehicles. DERs are capable of attractive time-shiftable behavior and of transacting reactive power and reserves in addition to real power. If DER capacity is optimally allocated among these three products, distribution network and economic benefits can be realized and renewable-related challenges can be mitigated, enabling increased renewable integration safety limits. In order to achieve optimal DER scheduling, this thesis proposes the formulation of a spatiotemporal marginal-cost based distribution power market and develops and implements tractable clearing algorithms. First, we formulate a centralized market clearing algorithm whose result is the optimal DER real power, reactive power and reserves schedules and the optimal nodal marginal costs. Our market formulation develops for the first time detailed and realistic models of the salient distribution network variable costs (transformer degradation, voltage sensitive loads) together with distribution network constraints (voltage bound constraints, that reflect distribution network congestion and AC load flow), and intertemporal DER dynamics and capabilities. However, the centralized algorithm does not scale, motivating the use of distributed algorithms. We propose two distributed algorithms: • A fully distributed algorithm that relies on massively parallel DER and distribution line specific sub-problem solutions, iteratively coordinated by nodal price estimates which promote and eventually enforce nodal balances. Upon convergence, nodal balances hold and optimal marginal costs are discovered. We further existing practices by using local penalty updates and stopping criteria that significantly reduce communication requirements. • A novel, partially distributed formulation in which DERs self-schedule in parallel based on centrally calculated price estimates, resulting from a load flow calculation. Nodal balances hold during all iterations. Finally, we are, to the best of our knowledge, the first to study voltage-constrained distribution market instances cleared with distributed methods. We decrease the deviation of marginal costs from their optimal values using first order optimality conditions and use voltage barrier functions for speedier convergence.2020-03-31T00:00:00

Proceedings of the XIII Global Optimization Workshop: GOW'16

[Excerpt] Preface: Past Global Optimization Workshop shave been held in Sopron (1985 and 1990), Szeged (WGO, 1995), Florence (GO’99, 1999), Hanmer Springs (Let’s GO, 2001), Santorini (Frontiers in GO, 2003), San José (Go’05, 2005), Mykonos (AGO’07, 2007), Skukuza (SAGO’08, 2008), Toulouse (TOGO’10, 2010), Natal (NAGO’12, 2012) and Málaga (MAGO’14, 2014) with the aim of stimulating discussion between senior and junior researchers on the topic of Global Optimization. In 2016, the XIII Global Optimization Workshop (GOW’16) takes place in Braga and is organized by three researchers from the University of Minho. Two of them belong to the Systems Engineering and Operational Research Group from the Algoritmi Research Centre and the other to the Statistics, Applied Probability and Operational Research Group from the Centre of Mathematics. The event received more than 50 submissions from 15 countries from Europe, South America and North America. We want to express our gratitude to the invited speaker Panos Pardalos for accepting the invitation and sharing his expertise, helping us to meet the workshop objectives. GOW’16 would not have been possible without the valuable contribution from the authors and the International Scientific Committee members. We thank you all. This proceedings book intends to present an overview of the topics that will be addressed in the workshop with the goal of contributing to interesting and fruitful discussions between the authors and participants. After the event, high quality papers can be submitted to a special issue of the Journal of Global Optimization dedicated to the workshop. [...

Study of computational method, Biopharmaceutics, Pharmacokinetics and Develop a Integrated Computational Prototype as Bioinformatics Application

Not availabl

Using Energy Landscape Theory to Uncover the Organization of Conformational Space of Proteins in Their Native States.

The functional motions of proteins navigate on rugged energy landscapes. Hence, mapping of these multidimensional landscapes into lower dimensional manifolds is imperative for gaining deeper insights into the functional dynamics. In the present work we implement novel computational schemes and means of analysis to characterize the topography of conformational space of selected proteins and also to elucidate their functional implications. The present thesis is divided into two parts, where we focus on the case studies of the intrinsically disordered histone tails and the representative allosteric protein Adenlyate Kinase. In particular, analyzing the energy landscapes of histone tails, we find preferential clustering of transient secondary structural elements in the conformational ensembles, which have a dramatic impact on the chain statistics, conformational dynamics and the binding pathways. In the study of Adenylate Kinase we use a novel nonlinear order parameter to rigorously estimate the free energy difference between allosteric states and map out the plausible pathway of transition, which reveals important structural and thermodynamic insights about the mechanism of allostery in Adenylate Kinase. Taken together our findings indicate that the organization of conformational space of functional proteins is delicately crafted to ensure efficient functional regulation and robust response to external signals

Discrete graphical models -- an optimization perspective

This monograph is about discrete energy minimization for discrete graphical models. It considers graphical models, or, more precisely, maximum a posteriori inference for graphical models, purely as a combinatorial optimization problem. Modeling, applications, probabilistic interpretations and many other aspects are either ignored here or find their place in examples and remarks only. It covers the integer linear programming formulation of the problem as well as its linear programming, Lagrange and Lagrange decomposition-based relaxations. In particular, it provides a detailed analysis of the polynomially solvable acyclic and submodular problems, along with the corresponding exact optimization methods. Major approximate methods, such as message passing and graph cut techniques are also described and analyzed comprehensively. The monograph can be useful for undergraduate and graduate students studying optimization or graphical models, as well as for experts in optimization who want to have a look into graphical models. To make the monograph suitable for both categories of readers we explicitly separate the mathematical optimization background chapters from those specific to graphical models.Comment: 270 page