Minimization with One Linear Equality Constraint and Bounds on the Variables |
Common terms and phrases
active set algebraic Algorithm for SLCP Appendix bound changes choice Cholesky factorization column computer storage condition number convergence corresponding denote density estimation descent direction diagonal matrix direction of negative equality constraint problem exact minimization feasible direction feasible point function evaluations Gill and Murray go to Step gradient H₂ inequality constraints iterate Iz Tv Lagrange multipliers LDLT Lemma line search linear constraints linear equality constraint matrix H minimize f(x null space numerical stability objective function orthogonal orthogonal matrix permutation matrix positive definite Proof quadratic programming regularized Newton method result search direction secant algorithm secant method secant update single linear equality solution special structure stationary point subproblem Suppose Theorem 3.2 triangular factorization Tv ² f unit lower triangular v²f(x vector vf(x ZTHZ zTv² f(x)Z zTvf(x