Now showing items 1-12 of 12

    • Characterization of Linear Complementarity Problems as Linear Programs 

      Mangasarian, Olvi (University of Wisconsin-Madison Department of Computer Sciences, 1976)
      It is shown that the linear complementarity problem of finding an n-by-1 vector x such that Mx + q > 0, x > 0, and xT(Mx+q) = 0, where M is a given n-by-n real matrix and q is a given n-by-l vector, is solvable if and ...
    • Characterizations of Bounded Solutions of Linear Complementarity Problems 

      Mangasarian, Olvi (University of Wisconsin-Madison Department of Computer Sciences, 1979)
    • Characterizations of Real Matrices of Monotone Kind 

      Mangasarian, Olvi (University of Wisconsin-Madison Department of Computer Sciences, 1968)
    • Convergent Generalized Monotone Splitting of Matrices 

      Mangasarian, Olvi (University of Wisconsin-Madison Department of Computer Sciences, 1970)
      Let B and T be n x n real matrices and r and n-vector and consider the system u = BTu+r. A new sufficient condition is given for the existence of a solution and convergence of a monotone process to a solution. The monotone ...
    • Equivalence of the Complementarity Problem to a System of Nonlinear Equations 

      Mangasarian, Olvi (University of Wisconsin-Madison Department of Computer Sciences, 1974)
    • Generalized Linear Complementarity Problems as Linear Programs 

      Mangasarian, Olvi (University of Wisconsin-Madison Department of Computer Sciences, 1978)
      A generalized linear complementarity problem which is equivalent to finding a root of a piecewise-linear system of equations is shown to be solvable if and only if a related linear programming problem is solvable. ...
    • Iterative Solution of Linear Programs 

      Mangasarian, Olvi (University of Wisconsin-Madison Department of Computer Sciences, 1978)
      By perturbing a linear program to a quadratic program it is possible to solve the latter in its dual variable space by iterative techniques such as successive over-relaxation (SOR) methods. This provides a solution to the ...
    • Linear Complementarity Problems Solvable by a Single Linear Program 

      Mangasarian, Olvi (University of Wisconsin-Madison Department of Computer Sciences, 1975)
      It is shown that the linear complementarity problem of finding a z in Rn such that Mz + q > 0, z > 0 and zT (Mz+q) = 0 can be solved by a single linear program in some important special cases such as when M or its inverse ...
    • Locally Unique Solutions of Quadratic Programs, Linear and Nonlinear Complementarity Problems 

      Mangasarian, Olvi (University of Wisconsin-Madison Department of Computer Sciences, 1979)
      It is shown that McCormick's second order sufficient optimality conditions are also necessary for a solution to a quadratic program to be locally unique and hence these conditions completely characterize a locally unique ...
    • Nonlinear Perturbation of Linear Programs 

      Mangasarian, Olvi; Meyer, Robert (University of Wisconsin-Madison Department of Computer Sciences, 1978)
      The objective function of any solvable linear program can be perturbed by a differentiable, convex or Lipschitz continuous function in such a way that (a) a solution of the original linear program is also a Karush-Kuhn-Tucker ...
    • Quadratic Convergence of a Newton Method for Nonlinear Programming 

      Mangasarian, Olvi (University of Wisconsin-Madison Department of Computer Sciences, 1972)
      A Newton algorithm for solving the problem minimize f(x) subject to g(x) - 0, where f:Rn - R and g:Rn - Rm is given for the case when g is concave. At each step a convex quadractic program with linear constraints is solved ...
    • Uniqueness of Solution in Linear Programming 

      Mangasarian, Olvi (University of Wisconsin-Madison Department of Computer Sciences, 1978)
      A number of characterizations are given which are both necessary and sufficient for the uniqueness of a solution to a linear programming problem.