In [19], we gave global convergence results for a second-derivative SQP method for minimizing the exact l1-merit function for a fixed value of the penalty parameter. To establish this result, we used the properties of the so-called Cauchy step, which was itself computed from the so-called predictor step. In addition, we allowed for the computation of a variety of (optional) SQP steps that were ...

penalty clause or liquidated damage which is formerly agreed between parties is legally examined and accepted as a rule. although judge could in some circumstances modify this stipulation. yet its economic analysis which is focused on economic efficiency can be considered as a “major unexplained puzzle in the economic theory of law”. this article compares the major legal systems in the case of ...

We construct an efficient numerical scheme for solving obstacle problems in divergence form. The numerical method is based on a reformulation of the obstacle in terms of an L1-like penalty on the variational problem. The reformulation is an exact regularizer in the sense that for a large (but finite) penalty parameter, we recover the exact solution. Our formulation is applied to classical ellip...

In this paper, we consider Newton's method for solving the system of necessary optimality conditions of optimization problems with equality and inequality constraints. The principal drawbacks of the method are the need for a good starting point, the inability to distinguish between local maxima and local minima, and, when inequality constraints are present, the necessity to solve a quadratic pr...

This paper reviews, extends and analyzes a new class of penalty methods for nonlinear optimization. These methods adjust the penalty parameter dynamically; by controlling the degree of linear feasibility achieved at every iteration, they promote balanced progress toward optimality and feasibility. In contrast with classical approaches, the choice of the penalty parameter ceases to be a heuristi...

We generalize the Metropolis et al. random walk algorithm to the situation where the energy is noisy and can only be estimated. Two possible applications are for long range potentials and for mixed quantum-classical simulations. If the noise is normally distributed, we are able to modify the acceptance probability by applying a penalty to the energy difference and thereby achieve exact sampling...

Article history: Received 17 September 2016 Received in revised form 2 March 2017 Accepted 2 March 2017 Available online 4 March 2017

In this article we study the simplest one-dimensional transport equation ut + aux = f and study the implementation of the boundary condition using a penalty