Browsing DMI Technical Reports by Title
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An optimization approach for radiosurgery treatment planning
(20011106)We outline a new approach for radiosurgery treatment planning, based on solving a series of optimization problems. We consider a speci c treat ment planning problem for a specialized device known as the Gamma Knife, ... 
Optimization of Gamma Knife Radiosurgery
(2000)The Gamma Knife is a highly specialized treatment unit that pro vides an advanced stereotactic approach to the treatment of tumors, vascular malformations, and pain disorders within the head. Inside a shielded ... 
A Practical Approach to Samplepath Simulation Optimization
(2000)We propose solving continuous parametric simulation optimizations using a deterministic nonlinear optimiza tion algorithm and samplepath simulations. The op timization problem is written in a modeling language with ... 
PrimalDual Bilinear Programming Solution of the Absolute Value Equation
(2011)We propose a finitely terminating primaldual bilinear programming algorithm for the solution of the NPhard absolute value equation (AVE): Ax ? x = b, where A is an n � n square matrix. The algorithm, which makes no ... 
PrivacyPreserving Classification of Horizontally Partitioned Data via Random Kernels
(2007)We propose a novel privacypreserving nonlinear support vector machine (SVM) classifier for a data matrix A whose columns represent input space features and whose individual rows are divided into groups of rows. Each ... 
PrivacyPreserving Classification of Vertically Partitioned Data via Random Kernels
(2007)We propose a novel privacypreserving support vector machine (SVM) classifier for a data matrix A whose input feature columns are divided into groups belonging to different entities. Each entity is unwilling to share its ... 
PrivacyPreserving Horizontally Partitioned Linear Programs
(2010)We propose a simple privacypreserving reformulation of a linear program whose equality constraint matrix is partitioned into groups of rows. Each group of matrix rows and its corresponding right hand side vector are ... 
PrivacyPreserving Linear and Nonlinear Approximation via Linear Programming
(2011)We propose a novel privacypreserving random kernel approximation based on a data matrix A ? Rm�n whose rows are divided into privately owned blocks. Each block of rows belongs to a different entity that is unwilling to ... 
PrivacyPreserving Random Kernel Classification of Checkerboard Partitioned Data
(2008)We propose a privacypreserving support vector machine (SVM) classifier for a data matrix A whose input feature columns as well as individual data point rows are divided into groups belonging to different entities. Each ... 
Probability of Unique Integer Solution to a System of Linear Equations
(2009)We consider a system of m linear equations in n variables Ax = d and give necessary and sufficient conditions for the existence of a unique solution to the system that is integer: x ? {?1,1}n. We achieve this by reformulating ... 
Proximal KnowledgeBased Classification
(20080626)Prior knowledge over general nonlinear sets is incor porated into proximal nonlinear kernel classification problems as linear equalities. The key tool in this incorporation is the conversion of general nonlinear prior ... 
Radiosurgery Treatment Planning via Nonlinear Programming
(200101)The Gamma Knife is a highly specialized treatment unit that pro vides an advanced stereotactic approach to the treatment of tumors, vascular malformations, and pain disorders within the head. Inside a shielded treatment ... 
Robust Linear and Support Vector Regression
(200009)The robust Huber Mestimator, a differentiable cost function that is quadratic for small errors and linear otherwise, is modeled exactly, in the original primal space of the problem, by an easily solvable simple convex ... 
RSVM: Reduced Support Vector Machines
(200101)An algorithm is proposed which generates a nonlinear kernelbased separating surface that requires as little as 1% of a large dataset for its explicit evaluation. To generate this nonlinear surface, the entire dataset ... 
Semismooth Support Vector Machines
(20001129)The linear support vector machine can be posed as a quadratic pro gram in a variety of ways. In this paper, we look at a formulation using the twonorm for the misclassi cation error that leads to a positive de  nite ... 
Set Containment Characterization
(2001)Characterization of the containment of a polyhedral set in a closed halfspace, a key factor in generating knowledgebased support vector machine classi ers [7], is extended to the following: (i) Containment of one ... 
SIMULATION OPTIMIZATION BASED ON A HETEROGENEOUS COMPUTING ENVIRONMENT
(2001)We solve a simulation optimization using a deterministic nonlinear solver based on the samplepath concept. The method used a quadratic model built from a collection of surrounding simulation points. The scheme does not ... 
Slice Models in General Purpose Modeling Systems
(20001214)Slice models are collections of mathematical programs with the same structure but di erent data. Examples of slice models appear in Data Envelopment Analysis, where they are used to evaluate e ciency, and crossvalidation, ... 
SSVM: A Amooth Support Vector Machine for Classification
(1999)Smoothing methods, extensively used for solving important math ematical programming problems and applications, are applied here to generate and solve an unconstrained smooth reformulation of the support vector machine ... 
Support Vector Machine Classi cation via Parameterless Robust Linear Programming
(2003)We show that the problem of minimizing the sum of arbitrarynorm real distances to misclassi ed points, from a pair of parallel bounding planes of a classi cation problem, divided by the margin (distance) be tween the ...