A Quantum Dual Logarithmic Barrier Method for Linear Optimization

It is known that predictor-corrector methods in a large neighborhood of the central path are among the most efficient interior-point methods (IPMs) for linear optimization (LO) problems. The best iteration bound based on the classical logarithmic barrier function is O(nlog (n/∊)). In this paper, we propose a family of self-regular proximity-based predictor-corrector (SRPC) IPMs for LO in a large neighborhood of the central path. In the predictor step, we use either an affine scaling or a self-regular direction; in the corrector step, we use always a self-regular direction. Our new algorithms use a special proximity function with different search directions and thus allows us to improve the so far best theoretical iteration complexity for a family of SRPC IPMs. An O\((\sqrt{n}{\exp} ((1 - q + {\log} n)/2) {\log} n {\log} (n/\epsilon))\) worst-case iteration bound with quadratic convergence is established, where q is the barrier degree of the SR proximity function.

The Mizuno–Todd–Ye algorithm in a larger neighborhood of the central path

A Busy March Meeting Is Brewing in Seattle

Today, more than ever, we need to examine the policy issues within RD it started as a $2 million/year expense and today remains a highly successful $100 million-plus high tech business. The principal output was spin-off companies, some unplanned, with over a $1 billion a year of new business. In short, successful R&D can make Hometown, U.S.A. rich. I'll return to this idea as a closer. In the United States, corporate R&D programs earn tax relief. Today we use many organization forms partnerships, separate firms, special-purpose contractors, and others. They don't affect the amount of relief, which is based on standard definitions from accountants: these rules contain contradictions. The basic notions as to deductibility of risk-laden expenses are sound within American expectations, which are for high returns. We can alter the legislative and thus the tax environment, and there are very large money consequences, for us as investors and as advisors. R&D is one of the several intangibles that affect the value of innovation in business. The National Innovation Initiative, a report of a recent convening of business leaders who are once again concerned for U.S. technical and business leadership, under the auspices of the Council on Competitiveness, is our current avenue for prompt influence and change in the innovation space. The agenda is rich, complex and offers much to all. Industrial Policy? Is there an over-riding U.S. Industrial Policy that provides an umbrella for the various elements in the complex NII agenda, and that thus dominates our choices? Our government expresses an official distaste for industrial policy when that is defined as the search for and selection of winners and national corporate champions. Subsidies and tariff protections are also contrary to World Trade Organization rules. So, officially, NO--the U.S. does not have an Industrial Policy. But what we do have to carry the Nil forward is called Private R&D, and it is so big that there are several policy influences, besides taxes, that affect our performance. What about performance? Do we do as well as we should? U.S. R&D expense has reached $300 billion per year. The Federal government buys or employs about $135 billion worth of work directly each year. This directed activity has impacted the entire U.S. R&D culture. There are some real successes, like the Defense Advanced Research Projects Agency (DARPA), some National Labs and the National Science Foundation. DARPA has altered industrial practice and even changed the pace of academia. The NSF has shown true leadership in its Engineering Research Centers program, a remarkable venture in contracted R&D with cost sharing by industry, a feature added through the intervention of the Industrial Research Institute into the rule-setting process. The National Labs offer clusters of large instruments to public access. The federal expenditure of about $135 billion is handled very much as a planned expense with a set of defined benefits, and this roadmap approach affects industrial practice. The U.S. National Academies join the process via consultation with the Congress, as they have for almost 150 years. Do Our Industrial Investments in R&D Work? The balance of the $300 billion total, less the federal direct outlay, or about $170 billion, is funded by industry through captive programs, new companies, partnerships, and registered collaborations, some multinational. Remember that the Congress and the Internal Revenue Service allow tax relief on all private R&D. Since statutory corporate tax rates are as high as 48 percent, the relief might amount to as much as $60 billion per year of concession on the remaining $170 billion of expenditures. …

This paper reports on how the US Defense Department has been slowly reducing its annual budget for computer science research in favor of near-term projects with a strictly military focus. While researchers can seek funding from the National Science Foundation (NSF), their grants tend to be smaller than compared to the Defense Advanced Research Projects Agency (DARPA), which appears to favor industry laboratories over the academia. Despite denials from DARPA officials, those familiar with budgetary decision making within the Pentagon say that there in fact has been a shift at DARPA, driven in large part by the country's ongoing conflicts in Iraq and Afghanistan. There are also those who believe that the IT industry, rather than the federal government, should sponsor its own research.

Rechargeable lithium-ion batteries have been extensively used in mobile communication and portable instruments due to their high volumetric and gravimetric energy density and low self-discharge rate, leading many scientists and engineers to work towards developing lithium-ion batteries with improved performance and longer life.In normal operation, an active solid-electrolyte-interface (SEI) layer forms in the first cycle of charging, due to reactions of lithium and solvent at the active surface (1,2). The SEI layer provides a barrier between the electrolyte and electrode to prevent further reaction while allowing lithium ions to permeate through the SEI layer in order to intercalate into and out of the bulk solid to store and release energy. However, the SEI layer continues to grow under repeated cycling. This growth increases the diffusion resistance of the lithium ions to the bulk active material, and removes cyclable lithium from the system, reducing the efficiency of the battery (1,2). This increased resistance can produce high temperature and can result in thermal runaway (3-5) within the battery. The properties and chemical composition of the SEI layer (active and passive) has been a subject of intense research due to its importance in the safety, capacity fade, and cycle life of Li-ion secondary batteries (6-12). Examination of the growth of the SEI layer as a mechanism for capacity fade has been performed using Kinetic Monte Carlo (KMC) simulations (13). This has provided valuable insight into the growth of the SEI layer and has shown the effects of high rates of charging on SEI layer passivation. These KMC simulations can be used to study the surface heterogeneity of the electrode surface as the passive layer is formed.The KMC model used will be expanded to a 2+1D model which tracks the thickness of the SEI layer over a representative surface of the solid particle. This will give a sense of the heterogeneity that arises in the SEI layer and will be coupled with the pseudo 2D model to simulate full battery operation. The P2D model will be converted from a system of partial differential equations to a system of ordinary differential equations by using reformulation techniques developed for the continuum model (14). The KMC model studies the events that occur in the SEI layer and the particle surface. For example, diffusion of the solvent in the SEI layer is modeled using the KMC approach. The reactions at the active material surface are modeled by considering the relative rate constants and using a random number generator to determine the event which occurs. In contrast, the continuum P2D model explains what happens in the bulk phases, and is deterministic. This coupled model will perform continuum calculations simultaneously with the KMC calculations. As passivation is considered in the KMC model, the capacity of the battery will fade with time, allowing for life time studies to be performed. This will lead to better understanding of the conditions which lead to capacity fade and better operation of lithium-ion batteries. Acknowledgements The authors acknowledge financial support by the National Science Foundation under grant numbers CBET-0828002, CBET-0828123, and CBET-1008692, and the Advanced Research Projects Agency – Energy (ARPA-E), U.S. Department of Energy, under Award Number DE-AR0000275.

Current communication architectures suffer from a growing collection of protocols in the host operating systems, gateways and applications, resulting in increasing implementation and maintenance cost, unreliability and difficulties with interoperability. The remote procedure call (RPC) approach has been used in some distributed systems to contain the diversity of application layer protocols within the procedure call abstraction. However, the same technique cannot be applied to lower layer protocols without violating the strict notion of layers.

In this paper, we study iteration complexities of Mizuno-Todd-Ye predictor-corrector (MTY-PC) algorithms in SDP and symmetric cone programs by way of curvature integrals. The curvature integral is defined along the central path, reflecting the geometric structure of the central path. Integrating curvature along the central path, we obtain a precise estimate of the number of iterations to solve the problem. It has been shown for LP that the number of iterations is asymptotically precisely estimated with the integral divided by $\sqrt{\beta}$ , where β is the opening parameter of the neighborhood of the central path in MTY-PC algorithms. Furthermore, this estimate agrees quite well with the observed number of iterations of the algorithm even when β is close to one and when applied to solve large LP instances from NETLIB. The purpose of this paper is to develop direct extensions of these two results to SDP and symmetric cone programs. More specifically, we give concrete formulas for curvature integrals in SDP and symmetric cone programs and give asymptotic estimates for iteration complexities. Through numerical experiments with large SDP instances from SDPLIB, we demonstrate that the number of iterations is explained quite well with the integral even for a large step size which is enough to solve practical large problems.

In this paper, we introduce the concept of trade-off ratio function, which is closely related to the well-known Geoffrion’s proper efficiency for multi-objective optimization problems, and investigate its boundedness property. For linear multi-objective optimization problems, we show that the trade-off ratio function is bounded on the efficient solution set. For piecewise linear multi-objective optimization problems, we show that all efficient solutions are always properly efficient in Borwein’s sense, and moreover, all efficient solutions are properly efficient in Geoffrion’s sense if and only if a recession condition holds. Finally, we provide an example to illustrate that the trade-off ratio function may be unbounded on the efficient solution set to piecewise linear multi-objective optimization problems, even if the recession condition holds, while it is bounded on the supported efficient solution set.

This is an excellent time for engineering design research. Not only is the National Science Foundation continuing its strong support for fundamental research in design but also the Department of Defense is pulling together a major new program in Engineered Resilient Systems at a level of funding that can completely change the field, and NASA's Langley Research Center is considering a new research thrust in complex engineered systems. Also, the Department of Defense sponsored Systems Engineering Research Center, a consortium of about two dozen universities, led by the Stevens Institute of Technology is conducting a substantial number of high quality research programs in systems engineering and continues to receive robust funding. And the Defense Advanced Research Projects Agency's Adaptive Vehicle Make program is committing hundreds of millions of dollars to demonstrate a radically new approach to design and development of complex systems.The impetus for all this funding is a crying need for more effective design. Research from my group at the University of Alabama in Huntsville, to be presented at this year's Conference on Systems Engineering Research, shows that the Department of Defense loses about $200 million per day in major weapon system cost overruns, program delays, and program reductions or cancellations. Experiences at NASA and Boeing, and at similar organizations outside the United States are essentially the same, although the Pentagon's programs are larger, more numerous, and better documented in the open literature (which is why we study them). I believe that the problems experienced by these programs are due to ineffective methods, processes, and tools.It is fair to ask how this can be, when the pages of this Journal are mainly devoted to disseminating the discovery and construction of design methods, processes, and tools. I see two reasons why our work to date has failed to stanch the bleeding of our largest engineering efforts. First, we do not have a way to measure the quality of methods, processes, and tools against a rigorous, widely accepted theory of design—in fact, we do not have such a theory. For large design projects performed within big organizations, we have hardly any theory useful for validating or comparing design methods. Second, the design theories we have do not sufficiently recognize the human, social, and organizational aspects of creating large systems.These two reasons are not problems for our research community. Instead, they are opportunities. We now have some nascent design theories circulating in our community with rigorous, sound foundations. The work is far from complete, but I think we have shown that we are up to it. And, we are making steady progress integrating learning from the social sciences into our design research. In fact, social-science based or linked design research is not at all new, but I believe it will become much more pervasive in the next few years.This is a new dawn in engineering design. Our field is on the verge of rapid growth into many deeply interesting areas. Hold your hats.Disclaimer: The opinions expressed in this piece are the author's alone. They do not necessarily reflect any positions of the National Science Foundation.

We extend coordinate descent to manifold domains and provide convergence analyses for geodesically convex and nonconvex smooth objective functions. Our key insight is to draw an analogy between coordinate blocks in Euclidean space and tangent subspaces of a manifold. Hence, our method is called tangent subspace descent (TSD). The core principle behind ensuring convergence of TSD is the appropriate choice of subspace at each iteration. To this end, we propose two novel conditions, the (C, r)-norm and C-randomized norm conditions on deterministic and randomized modes of subspace selection, respectively, that promise convergence for smooth functions and that are satisfied in practical contexts. We propose two subspace selection rules, one deterministic and another randomized, of particular practical interest on the Stiefel manifold. Our proof-of-concept numerical experiments on the sparse principal component analysis problem demonstrate TSD’s efficacy. Funding: This work was supported by the National Science Foundation [Grant 1740707] and the Defense Advanced Research Projects Agency Lagrange Program [Grant N660011824020].

Mapping the mind—smart thinking for brain health?

This document describes the results of a task force convened to determine what types of system software and tools were sufficiently important to warrant implementation across multiple vendors and machine types. The group included representatives from a wide range of user sites, as well as from the software development groups at vendor sites. Together, they established key software requirements, identified priorities for different types of user organizations, and formulated the requirements into language suitable for direct inclusion in procurements and requests-for-bids. The report is structured into four sections. The first discusses the formation and objectives of the task force and the processes used to arrive at consensus. Part 2 outlines the group's assumptions about how software will be specified on RFPs for parallel and clustered computers. In the next section, a tabular summary describes the requirements and the priority rank that was assigned to each. Part 4 presents the wording that is recommended for specifying each software element. Examples of how the requirements might be applied for various RFP scenarios, are in the appendices, which also provide vendor estimations of the level-of-effort required to develop and supply each requirement. The task force was sponsored by the Parallel Tools Consortium and the National Coordination Office for Computing, Information, and Communication. It was funded by grants from DoD HPC Modernization Program (NAVO Major Shared Resource Center), US Department of Energy, National Science Foundation, NASAS Ames Research Center, and Defense Advanced Research Projects Agency.

Large, sparse, linear systems of equations arise frequently when constructing mathematical models of natural phenomena. Most often, these linear systems are fully constrained and can be solved via direct or iterative techniques. However, one important problem class requires solutions to underconstrained linear systems that maximize some objective function. These linear optimization problems are natural formulations of many business plans and often contain hundreds of equations with thousands of variables. Historically, linear optimization problems have been solved via the simplex method. Despite the excellent performance of the simplex method, the size of the optimization problems and the frequency of their solution make linear optimization a computationally taxing endeavor. This paper examines the performance of parallel variants of the simplex algorithm on the Intel iPSC, a message-based parallel system. Linear optimization test data are drawn from commercial sources and represent realistic problems. Analysis shows that the speedup obtained is sensitive to both the structure of the underlying data and the data partitioning.

Voltage profile improvement and loss reduction is an important issue in power system especially under loaded condition. In this paper, two FACTS controllers like Static Var Compensator (SVC), and Thyristor Controlled Series Capacitor (TCSC) are considered for voltage profile improvement and loss reduction. The voltage profile improvement and loss reduction using FACTS devices is a problem of combinatorial non linear optimization. Small population based particle swarm optimization (SPPSO) has been used to solve this combinatorial non linear optimization problem. To enhance the diversity of particle in small population, mutation operator and concept of regeneration is used. The optimizations are performed on two parameters: the location and the values of SVC and TCSC. The proposed method is tested on modified IEEE 30 bus system for two operating conditions. To validate the accuracy of results a comparison with conventional particle swarm optimization (CPSO) has been made. The results show the effectiveness of SPPSO than CPSO in loss reduction and voltage profile improvement.