Now showing items 28-46 of 46

    • A Practical Approach to Sample-path Simulation Optimization 

      Munson, Todd; Ferris, Michael (2000)
      We propose solving continuous parametric simulation optimizations using a deterministic nonlinear optimiza- tion algorithm and sample-path simulations. The op- timization problem is written in a modeling language with ...
    • Primal-Dual Bilinear Programming Solution of the Absolute Value Equation 

      Mangasarian, Olvi (2011)
      We propose a finitely terminating primal-dual bilinear programming algorithm for the solution of the NP-hard absolute value equation (AVE): Ax ? |x| = b, where A is an n � n square matrix. The algorithm, which makes no ...
    • Privacy-Preserving Classification of Horizontally Partitioned Data via Random Kernels 

      Wild, E; Mangasarian, Olvi (2007)
      We propose a novel privacy-preserving 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 ...
    • Privacy-Preserving Classification of Vertically Partitioned Data via Random Kernels 

      Fung, Glenn; Wild, Edward; Mangasarian, Olvi (2007)
      We propose a novel privacy-preserving 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 ...
    • Privacy-Preserving Horizontally Partitioned Linear Programs 

      Mangasarian, Olvi (2010)
      We propose a simple privacy-preserving 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 ...
    • Privacy-Preserving Linear and Nonlinear Approximation via Linear Programming 

      Mangasarian, Olvi; Fung, Glenn (2011)
      We propose a novel privacy-preserving 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 ...
    • Privacy-Preserving Random Kernel Classification of Checkerboard Partitioned Data 

      Wild, Edward; Mangasarian, Olvi (2008)
      We propose a privacy-preserving 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 

      Recht, Benjamin; Mangasarian, Olvi (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 Knowledge-Based Classification 

      Fung, Glenn; Wild, Edward; Mangasarian, Olvi (2008-06-26)
      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 

      Shepard, David; Lim, Jinho; Ferris, Michael (2001-01)
      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 

      Musicant, David; Mangasarian, Olvi (2000-09)
      The robust Huber M-estimator, 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 

      Mangasarian, Olvi; Lee, Yuh-Jye (2001-01)
      An algorithm is proposed which generates a nonlinear kernel-based 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 

      Munson, Todd; Ferris, Michael (2000-11-29)
      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 two-norm for the misclassi cation error that leads to a positive de - nite ...
    • Set Containment Characterization 

      Mangasarian, Olvi (2001)
      Characterization of the containment of a polyhedral set in a closed halfspace, a key factor in generating knowledge-based support vector machine classi ers [7], is extended to the following: (i) Containment of one ...
    • SIMULATION OPTIMIZATION BASED ON A HETEROGENEOUS COMPUTING ENVIRONMENT 

      Ferris, Michael; Sinapiromsaran, Krung (2001)
      We solve a simulation optimization using a deterministic nonlinear solver based on the sample-path 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 

      Meta, Voelker; Ferris, Michael (2000-12-14)
      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 cross-validation, ...
    • SSVM: A Amooth Support Vector Machine for Classification 

      Mangasarian, Olvi; Lee, Yuh-Jye (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 

      Mangasarian, Olvi (2003)
      We show that the problem of minimizing the sum of arbitrary-norm 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 ...
    • Survival-Time Classi cation of Breast Cancer Patients 

      Wolberg, William; Mangasarian, Olvi; Lee, Yuh-Jye (2001)
      The identi cation of breast cancer patients for whom chemother- apy could prolong survival time is treated here as a data mining prob- lem. This identi cation is achieved by clustering 253 breast cancer patients into ...