Browsing CS Technical Reports by Author "Mangasarian, Olvi"
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Characterization of Linear Complementarity Problems as Linear Programs
Mangasarian, Olvi (University of WisconsinMadison Department of Computer Sciences, 1976)It is shown that the linear complementarity problem of finding an nby1 vector x such that Mx + q > 0, x > 0, and xT(Mx+q) = 0, where M is a given nbyn real matrix and q is a given nbyl vector, is solvable if and ... 
Characterizations of Bounded Solutions of Linear Complementarity Problems
Mangasarian, Olvi (University of WisconsinMadison Department of Computer Sciences, 1979) 
Characterizations of Real Matrices of Monotone Kind
Mangasarian, Olvi (University of WisconsinMadison Department of Computer Sciences, 1968) 
Convergent Generalized Monotone Splitting of Matrices
Mangasarian, Olvi (University of WisconsinMadison Department of Computer Sciences, 1970)Let B and T be n x n real matrices and r and nvector 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 WisconsinMadison Department of Computer Sciences, 1974) 
Generalized Linear Complementarity Problems as Linear Programs
Mangasarian, Olvi (University of WisconsinMadison Department of Computer Sciences, 1978)A generalized linear complementarity problem which is equivalent to finding a root of a piecewiselinear 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 WisconsinMadison 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 overrelaxation (SOR) methods. This provides a solution to the ... 
Linear Complementarity Problems Solvable by a Single Linear Program
Mangasarian, Olvi (University of WisconsinMadison 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 WisconsinMadison 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 WisconsinMadison 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 KarushKuhnTucker ... 
Quadratic Convergence of a Newton Method for Nonlinear Programming
Mangasarian, Olvi (University of WisconsinMadison 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 WisconsinMadison 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.