Interior Point Methods for Massive Support Vector Machines

We investigate the use of interior point methods for solving quadratic programming problems with a small number of linear constraints where the quadratic term consists of a low-rank update to a positive semi-de nite matrix. Several formulations of the support vector machine t into this category. An interesting feature of these particular problems is the vol- ume of data, which can lead to quadratic programs with between 10 and 100 million variables and a dense Q matrix. We use OOQP, an object- oriented interior point code, to solve these problem because it allows us to easily tailor the required linear algebra to the application. Our linear algebra implementation uses a proximal point modi cation to the under- lying algorithm, and exploits the Sherman-Morrison-Woodbury formula and the Schur complement to facilitate e cient linear system solution. Since we target massive problems, the data is stored out-of-core and we overlap computation and I/O to reduce overhead. Results are reported for several linear support vector machine formulations demonstrating the reliability and scalability of the method

Bending a Beam to Significantly Reduce Wakefields of Short Bunches

A method of significantly reducing wakefields generated at collimators is proposed, in which the path of a beam is slightly bent before collimation. This is applicable for short bunches and can reduce the wakefields by a factor of around 7 for present day free electron lasers and future colliders.Comment: 12 pages, 5 figure

Human-centered Electric Prosthetic (HELP) Hand

Through a partnership with Indian non-profit Bhagwan Mahaveer Viklang Sahayata Samiti, we designed a functional, robust, and and low cost electrically powered prosthetic hand that communicates with unilateral, transradial, urban Indian amputees through a biointerface. The device uses compliant tendon actuation, a small linear servo, and a wearable garment outfitted with flex sensors to produce a device that, once placed inside a prosthetic glove, is anthropomorphic in both look and feel. The prosthesis was developed such that future groups can design for manufacturing and distribution in India

Mathematical programs with equilibrium constraints: automatic reformulation and solution via constrained optimization

Constrained optimization has been extensively used to solve many large scale deterministic problems arising in economics, including, for example, square systems of equations and nonlinear programs. A separate set of models have been generated more recently, using complementarity to model various phenomenon, particularly in general equilibria. The unifying framework of mathematical programs with equilibrium constraints (MPEC) has been postulated for problems that combine facets of optimization and complementarity. This paper briefly reviews some methods available to solve these problems and described a new suite of tools for working with MPEC models. Computational results demonstrating the potential of this tool are given that automatically construct and solve a variety of different nonlinear programming reformulations of MPEC problems.\ud \ud This material is based on research partially supported by the National Science Foundation Grant CCR-9972372, the Air Force Office of Scientific Research Grant F49620-01-1-0040, Microsoft Corporation and the Guggenheim Foundation

Neuro-Dynamic Programming for Radiation Treatment Planning

In many cases a radiotherapy treatment is delivered as a series of smaller dosages over a period of time. Currently, it is difficult to determine the actual dose that has been delivered at each stage, precluding the use of adaptive treatment plans. However, new generations of machines will give more accurate information of actual dose delivered, allowing a planner to compensate for errors in delivery. We formulate a model of the day-to-day planning problem as a stochastic linear program and exhibit the gains that can be achieved by incorporating uncertainty about errors during treatment into the planning process. Due to size and time restrictions, the model becomes intractable for realistic instances. We show how neuro-dynamic programming can be used to approximate the stochastic solution, and derive results from our models for realistic time periods. These results allow us to generate practical rules of thumb that can be immediately implemented in current planning technologies.\ud \ud This material is based on research partially supported by the National Science Foundation Grants ACI-0113051 and CCR-9972372, the Air Force Office of Scientific Research Grant F49620-01-1-0040, Microsoft Corporation and the Guggenheim Foundation