This study containsa new approach to the unconstrained minimization of a multivariable function f(.) using a quasi-Newton step computation procedure. The whole problem is reformulated as the control problem of a linear system described by its state-space equations and having unknown dynamical properties. First of all, an adaptive identification problem arises and is solved by using set estimati...

• Significant correlations between age group and performance for FRs (r=0.55, p<0.001) and PDDs (r=0.56, p<0.001). 2. Truth-Value Judgment Task Methods •Participants: 4yo (18), 5yo (17), 6yo (19), 7yo (11). •Participants were told: “Cookie Monster really likes cookies, but he does NOT like onions.” They were shown pictures of (i) plates of cookies, (ii) onions, or (iii) both cookies and onions....

A cutting plane method for linear/convex programming is described. It is based on the volumetric barrier, introduced by Vaidya. The algorithm is a long step one, and has a complexity of O(nL) Newton steps. This is better than the O(n √ mL) complexity of non-cutting plane long step methods based on the volumetric barrier, but it is however worse than Vaidya’s original O(nL) result (which is not ...

In this paper we propose a new class of primal-dual path-following interior point algorithms for solving monotone linear complementarity problems. At each iteration, the method would select a target on the central path with a large update from the current iterate, and then the Newton method is used to get the search directions, followed by adaptively choosing the step sizes, which are e.g. the ...

The Kantorovich Theorem is a fundamental tool in nonlinear analysis which has been extensively used in classical numerical analysis. In this paper we show that it can also be used in analyzing interior point methods. We obtain optimal bounds for Newton’s method when relied upon in a path following algorithm for linear complementarity problems. Given a point z that approximates a point z(τ ) on ...

Quasi-Newton methods based on least change secant updating formulas that solve linear equations Ax = b in n = dim(x) = dim(b) steps can be expected to solve corresponding smooth nonlinear systems n-step quadratically, i.e. with an r-order of ρ = 2 = 1 + 1/n+O(1/n). The best rate one can possibly expect on general problems is given by the positive root ρn of ρ (ρ− 1) = 1, for which ρn − 1 = ln(n...

We consider the numerical solution of discretised Hamilton-Jacobi-Bellman (HJB) equations with applications in finance. For the discrete linear complementarity problem arising in American option pricing, we study a policy iteration method. We show, analytically and numerically, that, in standard situations, the computational cost of this approach is comparable to that of European option pricing...

A major problem in obtaining an efficient implementation of fully implicit RungeKutta (IRK) methods applied to systems of differential equations is to solve the underlying systems of nonlinear equations. Their solution is usually obtained by application of modified Newton iterations with an approximate Jacobian matrix. The systems of linear equations of the modified Newton method can actually b...

A major problem in obtaining an efficient implementation of fully implicit RungeKutta (IRK) methods applied to systems of differential equations is to solve the underlying systems of nonlinear equations. Their solution is usually obtained by application of modified Newton iterations with an approximate Jacobian matrix. The systems of linear equations of the modified Newton method can actually b...

In this paper we discuss Pantoja's construction of the Newton direction for discrete time optimal control problems. We show that Automatic Diierentiation techniques can be used to calculate the Newton direction accurately, without requiring extensive rewriting of user code, and at a surprisingly low computational cost: for an N-step problem with p control variables and q state variables at each...