The steepest descent gravitational method for linear programming
نویسندگان
چکیده
منابع مشابه
The steepest descent gravitational method for linear programming
We present a version of the gravitational method for linear programming, based on steepest descent gravitational directions. Finding the direction involves a special small “nearest point problem” that we solve using an efficient geometric approach. The method requires no expensive initialization, and operates only with a small subset of locally active constraints at each step. Redundant constra...
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u̇(t) = −∇xf(u(t), r(t)), u(t0) = u0 where f(x, r) is the exponential penalty function associated with the linear program min{c′x : Ax ≤ b}, and r(t) decreases to 0 as t goes to ∞. We show that for each initial condition (t0, u0) the solution u(t) is defined on the whole interval [t0,∞) and, under suitable hypothesis on the rate of decrease of r(t), we establish the convergence of u(t) towards a...
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متن کاملOn the Steepest Descent Method for Matrix
We consider the special case of the restarted Arnoldi method for approximating the product of a function of a Hermitian matrix with a vector which results when the restart length is set to one. When applied to the solution of a linear system of equations, this approach coincides with the method of steepest descent. We show that the method is equivalent with an interpolation process in which the...
متن کاملOn the Steepest Descent Method for Matrix
We consider the special case of the restarted Arnoldi method for approximating the product of a function of a Hermitian matrix with a vector which results when the restart length is set to one. When applied to the solution of a linear system of equations, this approach coincides with the method of steepest descent. We show that the method is equivalent with an interpolation process in which the...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1989
ISSN: 0166-218X
DOI: 10.1016/0166-218x(89)90002-4