Now showing items 21-40 of 46

    • 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 ...
    • 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 ...
    • Absolute Value Equation Solution via Dual Complementarity 

      Mangasarian, Olvi (2011)
      By utilizing a dual complementarity condition, we propose an iterative method for solving the NPhard absolute value equation (AVE): Ax?|x| = b, where A is an n�n square matrix. The algorithm makes no assumptions on the ...
    • Equivalence of Minimal L0 and Lp Norm Solutions of Linear Equalities, Inequalities and Linear Programs for Sufficiently Small p 

      Mangasarian, Olvi; Fung, Glenn (2011)
      For a bounded system of linear equalities and inequalities we show that the NP-hard ?0 norm minimization problem min ||x||0 subject to Ax = a, Bx ? b and ||x||? ? 1, is completely equivalent to the concave minimization ...
    • 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 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 ...
    • 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 ...
    • 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 ...
    • 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 ...
    • Exactness Conditions for a Convex Differentiable Exterior Penalty for Linear Programming 

      Wild, Edward; Mangasarian, Olvi (2007)
      Sufficient conditions are given for a classical dual exterior penalty function of a linear program to be independent of its penalty parameter. This ensures that an exact solution to the primal linear program can be obtained ...
    • Chunking for Massive Nonlinear Kernel Classification 

      Thompson, Michael; Mangasarian, Olvi (2006)
      A chunking procedure [2] utilized in [18] for linear classifiers is proposed here for nonlinear kernel classification of massive datasets. A highly accurate algorithm based on nonlinear support vector machines that ...
    • 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 ...
    • Nonlinear Knowledge-Based Classification 

      Wild, Edward; Mangasarian, Olvi (2006)
      Prior knowledge over general nonlinear sets is incorporated into nonlinear kernel classification problems as linear constraints in a linear program. The key tool in this incorporation is a theorem of the alternative for ...
    • Massive Data Classification via Unconstrained Support Vector Machines 

      Thompson, Michael; Mangasarian, Olvi (2006)
      A highly accurate algorithm, based on support vector machines formulated as linear programs [13, 1], is proposed here as a completely unconstrained minimization problem [15]. Combined with a chunking procedure [2] this ...
    • Absolute Value Equations 

      Meyer, Robert; Mangasarian, Olvi (2005)
      We investigate existence and nonexistence of solutions for NP-hard equations in- volving absolute values of variables: Ax ? |x| = b, where A is an arbitrary n � n real matrix. By utilizing an equivalence relation to the ...
    • 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 ...
    • Lagrangian Support Vector Machines 

      Musicant, David; Mangasarian, Olvi (2000)
      An implicit Lagrangian for the dual of a simple reformulation of the standard quadratic program of a linear support vector machine is proposed. This leads to the minimization of an unconstrained di erentiable convex ...
    • Interior Point Methods for Massive Support Vector Machines 

      Munson, Todd; Ferris, Michael (2000-05-25)
      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. ...
    • 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 ...