Global error bounds for convex conic problems

In this paper Lipschitzian type error bounds are derived for general convex conic problems under various regularity conditions. Specifically, it is shown that if the recession directions satisfy Slater's condition then a global Lipschitzian type error bound holds. Alternatively, if the feasible region is bounded, then the ordinary Slater condition guarantees a global Lipschitzian type error bound. These can be considered as generalizations of previously known results for inequality systems. Moreover, some of the results are also generalized to the intersection of multiple cones. Under Slater's condition alone, a global Lipschitzian type error bound may not hold. However, it is shown that such an error bound holds for a specific region. For linear systems we show that the constant involved in Hoffman's error bound can be estimated by the so-called condition number for linear programming

The marketing orientation of small and medium enterprises: An Australian study

The market orientation construct has emerged as a key marketing theme in the 1990\u27s. While the concept of being focussed on the market (customers and competitors) has been known since the early 1950\u27s (e.g. Drucker,1954), putting the concept into practice through a set of specific actions has eluded many organisations and academics. As a result, market orientation (also termed market focus, customer focus and competitor focus) had remained a business philosophy (Bennett & Cooper, 1979: Felton, 1959; Konopa & Calabro,1971) more than a strategic approach. While there have been sporadic attempts at defining or operationalisinga marketing or customer orientation in the past (Gronrnos, 1989: Kotler, 1977: Masiello, 1988: Webster,1988), the first serious effort in the early 1990\u27s when Kohli and Jaworski (1990) and Narver and Slater (1990 defined market orientation as a set of organisational activities or behaviours. Narver and Slater also found a positive link between having such an orientation and business performance. The emphasis in both models was on obtaining and understanding customers and competitors and responding to customers\u27 needs better than competitors through a coordinated effort across the organisation. Subsequently a number of studies have supported the positive relationship between market orientation and business performance. However, results have not been consistent and several variables have been shown to moderate the market orientation performance relationship. All of the major market orientation studies have been undertaken within large organisations and very little is known about the market orientation of small and medium enterprises (SMEs), or of its relationship to their performance. It is recognised that SMEs are different from large businesses some of their marketing practices are unique to SME. Given this uniqueness, the present research examined the applicability of existing market orientation constructs and models to SMEs. For this purpose, Kohli and Jaworski\u27s and Narver and Slater\u27s constructs were modified and some unique SME items were added. Following a staged research approach, as recommended by Churchill (1979), a randomly chosen sample of Australian SMEs was surveyed. In all, more than 700 responses were received, of which 542, were used in the present study. The results obtained suggested that while a form of market orientation existed in SMEs, its operationalisation was different. Of Kohli and Jaworski’s (1990) three dimensions, (intelligence generation, dissemination and organisational response), organisational response could not be supported. The study also provided support for Narver and Slater\u27s (1990) customer and competitor orientation constructs. The third construct \u27inter-functional coordination\u27 was not included as early qualitative interviews made it clear that it had no meaning in an SME context. Customer and competitor orientations emerged as distinct constructs but the interrelationship between the two suggested the presence of a higher order \u27market orientation\u27 construct. Compared to the organisations analysed in earlier studies, the SMEs in the current study were small in size and very few had multiple functional areas. In most of the businesses, marketing did not exist as a separate function. Consequently there was 110 support for constructs such as organisational response and inter-functional coordination. The informal nature of SMEs marketing activities was evident in the market orientation constructs. It appeared that SMEs collect their intelligence through informal means. Their marketing activities were also based more on intuition than logic. Apart from customer and competitor orientations, a customer service orientation emerged as an important element. Having a customer service orientation led to customer satisfaction and, hence, to repeal business, which was considered to be extremely important by the small businesses surveyed. Having a customer service orientation also had a positive impact on the organisational commitment of employees, repeat business and business performance. The overall impact of customer orientation and competitor orientation on business performance was positive, but small. This was not surprising as respondents took a casual or intuitive approach to marketing. It seems that small business performance is constrained by factors other than marketing, such as the availability of resources. Further, even among large businesses. The market orientation-performance relationship has not been consistently positive or significant. The present results suggest that market orientation, as practised in large businesses, or as articulated by academics, may not be applicable to SMEs and that customer service elements needed to be included in the model. As regards performance, the results obtained suggest that factors other than marketing are also critical and fun her research is needed to tease out the nature of these additional factors

Interactive Medical Image Registration With Multigrid Methods and Bounded Biharmonic Functions

Interactive image registration is important in some medical applications since automatic image registration is often slow and sometimes error-prone. We consider interactive registration methods that incorporate user-specified local transforms around control handles. The deformation between handles is interpolated by some smooth functions, minimizing some variational energies. Besides smoothness, we expect the impact of a control handle to be local. Therefore we choose bounded biharmonic weight functions to blend local transforms, a cutting-edge technique in computer graphics. However, medical images are usually huge, and this technique takes a lot of time that makes itself impracticable for interactive image registration. To expedite this process, we use a multigrid active set method to solve bounded biharmonic functions (BBF). The multigrid approach is for two scenarios, refining the active set from coarse to fine resolutions, and solving the linear systems constrained by working active sets. We\u27ve implemented both weighted Jacobi method and successive over-relaxation (SOR) in the multigrid solver. Since the problem has box constraints, we cannot directly use regular updates in Jacobi and SOR methods. Instead, we choose a descent step size and clamp the update to satisfy the box constraints. We explore the ways to choose step sizes and discuss their relation to the spectral radii of the iteration matrices. The relaxation factors, which are closely related to step sizes, are estimated by analyzing the eigenvalues of the bilaplacian matrices. We give a proof about the termination of our algorithm and provide some theoretical error bounds. Another minor problem we address is to register big images on GPU with limited memory. We\u27ve implemented an image registration algorithm with virtual image slices on GPU. An image slice is treated similarly to a page in virtual memory. We execute a wavefront of subtasks together to reduce the number of data transfers. Our main contribution is a fast multigrid method for interactive medical image registration that uses bounded biharmonic functions to blend local transforms. We report a novel multigrid approach to refine active set quickly and use clamped updates based on weighted Jacobi and SOR. This multigrid method can be used to efficiently solve other quadratic programs that have active sets distributed over continuous regions

The quantum theory of antiferromagnetism

"This report is based on a Doctoral thesis in the department of Physics, Massachusetts Institute of Technology."Bibliography: p. 31.Army Signal Corps Contract No. W-36-039 sc-32037. Dept. of the Army Project No. 3-99-10-022.[by] R.J. Harrison

The Legacies of Deindustrialization and the Blackstone River Valley National Heritage Corridor

Creation of the Blackstone River Valley National Heritage Corridor and release of a master plan for cultural and physical resource development is creating a new standard for private, local, state, and federal partnerships. Actions by the Corridor\u27s partners are shaped by both past and contemporary economic development issues. Using tools of humanistic inquiry — history, economics, preservation, sociology, political science — for social and economic purposes signifies far-reaching shifts and possibilities for public planning and policy philosophies in both public and private agencies

Decision analysis: vector optimization theory

First published in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales in 93, 4, 1999, published by the Real Academia de Ciencias Exactas, Físicas y Naturales

The R-algebra of Quasiknowledge and Convex Optimization

This article develops a convex description of a classical or quantum learner's or agent's state of knowledge about its environment, presented as a convex subset of a commutative R-algebra. With caveats, this leads to a generalization of certain semidefinite programs in quantum information (such as those describing the universal query algorithm dual to the quantum adversary bound, related to optimal learning or control of the environment) to the classical and faulty-quantum setting, which would not be possible with a naive description via joint probability distributions over environment and internal memory. More philosophically, it also makes an interpretation of the set of reduced density matrices as "states of knowledge" of an observer of its environment, related to these techniques, more explicit. As another example, I describe and solve a formal differential equation of states of knowledge in that algebra, where an agent obtains experimental data in a Poissonian process, and its state of knowledge evolves as an exponential power series. However, this framework currently lacks impressive applications, and I post it in part to solicit feedback and collaboration on those. In particular, it may be possible to develop it into a new framework for the design of experiments, e.g. the problem of finding maximally informative questions to ask human labelers or the environment in machine-learning problems. The parts of the article not related to quantum information don't assume knowledge of it.Comment: 40 page

Optimization in semi-supervised classification of multivariate time series

Abstract. In this thesis, I study methods that classify time series in a semi-supervised manner. I compare the performance of models that assume independent and identically distributed observations against models that assume nearby observations to be dependent of each other. These models are evaluated on three real world time series data sets. In addition, I carefully go through the theory of mathematical optimization behind two successful algorithms used in this thesis: Support Vector Data Description and Dynamic Time Warping. For the algorithm Dynamic Time Warping, I provide a novel proof that is based on dynamic optimization. The experiments in this thesis suggest that the assumption of observations in time series to be independent and identically distributed may deteriorate the results of semi-supervised classification. The novel self-training method presented in this thesis called Peak Evaluation using Perceptually Important Points shows great performance on multivariate time series compared to the methods currently existing in literature. The feature subset selection of multivariate time series may improve classification performance, but finding a reliable unsupervised feature subset selection method remains an open question