A Parameter-free Penalty Method for Solving the Linear Programming Problem |
Contents
PARAMETERFREE PENALTY METHOD | 12 |
3 | 18 |
PARAMETERFREE PENALTY METHOD USING BASIS MATRICES | 37 |
3 other sections not shown
Common terms and phrases
A₁ A₂ active rows AK+1 algorithm APPENDIX arbitrary parameter Ax+1 B¯¹N b₁ b¹y Bartels basic feasible point c¹x columns of Q component compute Conn Conn's Consider the L.P. constraint matrix corner d₁ d₂ descent direction dual find a descent FORTRAN Hence identity matrix iɛI iɛIA index sets jth column L.P. problem line search Linear Algebra linear programming problem m x m m x n minimize cTx subject minimize p(x n x n n x t optimization problem orthogonal overdetermined system PARAMETER-FREE PENALTY METHOD penalty function phase primal problem minimize cTx projection matrix Q₁ Q₂ QR decomposition Rotation Rx+1 scheme sequence of Givens simplex algorithm Simplex method solution STEP storage subject to Ax Suppose a column t₁ t₂ TEMP2 Theorem transformations Update upper triangular form Vp(x XXXX XXX zero vector Αλ