Numerical Methods for Constrained OptimizationPhilip E. Gill, P. E. Gill, William Allan Murray, Institute of Mathematics and Its Applications, National Physical Laboratory (Great Britain) |
Common terms and phrases
active constraints active set algorithm barrier function basis Chapter Cholesky factors compute condition number d₁ defined deleted descent direction diagonal direct-search direction of search efficient equality constraints equations estimates evaluations feasible point feasible region fill-in Fletcher formula Gill and Murray given Goldfarb gradient Hessian matrix implies inactive constraints inverse iteration jth column Lagrange multipliers Lagrangian function linear constraints linear programming linearly constrained problem linearly independent LQ factorization matrix G minimize F(x modified Newton method non-singular non-zero elements nonlinear constraints nonlinear programming objective function obtained orthogonal parameter penalty function positive definite procedure projection quadratic approximation quadratic function quadratic programming quasi-Newton methods rate of convergence reduced rows scalar search direction second derivatives second-order Section sequence simplex solution solving sparse sparse matrix stationary point step steplength storage strategy strong local minimum techniques Theorem unconstrained minimization updating variables vector vertex zero