Abstract—The solution of non linear problems are based on very well grounded mathematical theories. This document proposes a Newton step graph-based model for convex non linear separable problems (NLP) with linear constraints. The Newton step is well suited for this kind of problems, but when the problem size grows the NLSP model will grow in a non linear manner. Furthermore, the constraints ha...

This paper focuses on the weighted complementarity problem (WCP), which is widely used in fields of economics, sciences and engineering. Not least because its local superlinear convergence rate, smoothing Newton methods have widespread application solving various optimization problems. A two-step method with strong proposed. With a complementary function, WCP reformulated as set equations solve...

From the constraint imposition aspects in 3D to friction regularization, various ideas are exposed in this paper. A variation of the Rockafellar Lagrangian is proposed which results in continuous second-order derivatives if Lagrange multiplier estimates are greater or equal than one. This fact allows the adoption of a full second-order (i.e. Lagrange–Newton) method avoiding sequential unconstra...

We compare the Ostrowski efficiency of some methods for solving systems of nonlinear equations without explicitly using derivatives. The methods considered include the discrete Newton method, Shamanskii’s method, the two-point secant method, and Brown’s methods. We introduce a class of secant methods and a class of methods related to Brown’s methods, but using orthogonal rather than stabilized ...

A fully variational approach is developed for solving nonlinear elliptic equations that enables accurate discretization and fast solution methods. The equations are converted to a first-order system that is then linearized via Newton’s method. First-order system least squares (FOSLS) is used to formulate and discretize the Newton step, and the resulting matrix equation is solved using algebraic...

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...