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Step Length Determination
Variable Metric Updates
12 other sections not shown
Algorithm 7A assumed bang-bang control bang-bang principle holds BFGS method boundary condition bounded Chapter condition number conditional gradient method conjugate gradient method constraints convergence rate convex set cost function define descent direction differential equations eigenvalues exact step F(ui Frechet differentiable given global convergence Hence Hilbert space implies inf F(u inventory iteration LEMMA Let F linear convergence linearly independent Lipschitz continuous Math mean value theorem nonlinear nonlinear programming norm obtain operator optimal control optimal control problems optimal point optimization problem orbit positive definite production quadratic quasi-Newton methods satisfied self-adjoint solution step length rule step size rule strong uniqueness superlinear convergence switching points t e 0,T u e H ui+1 Ul Ul Ul V F(u variable metric methods vector VF(u VF(ui yields zero Zoutendijk condition