Exterior Penalty Function Method Research Articles

Effect of manufacturing tolerances on indexing accuracy and synthesis of the Geneva Mechanism

Machine tools used for batch and mass production are generally equipped with the Geneva Mechanism for indexing. One of the factors affecting the machining accuracy in these machine tools is the positional accuracy of the tools with respect to the work which, in turn, is affected by the indexing accuracy of the indexing mechanism. This paper discusses the effect of manufacturing tolerances on indexing accuracy. It is observed that indexing accuracy is different for constrained and unconstrained designs corresponding to the same value of tolerance. Results regarding indexing accuracy for different values of tolerances in constrained designs are recorded and suggest that, in the case of constrained designs, careful allocation of tolerances on design parameters is needed. The method of tolerance allocation suggested by Choubey and Atluri 8 is followed. Synthesis of a six-slot Geneva Mechanism incorporating manufacturing tolerances and following stochastic non-linear programming and the exterior penalty function method is carried out to study these effects. Practical implications of the effects of manufacturing tolerances on indexing accuracy and synthesis of Geneva drives are discussed, giving suitable examples

Alternative approaches to the machining parameter optimization problem

Several nonlinear programming techniques may be used in solving the machining parameter problem for optimal values of speed, feed, and depth of cut. These techniques vary widely in efficiency and ease of implementation. Five techniques are described and two, SUMT and an Exterior Penalty Function method, are compared through an example problem. The latter approach is found to be more efficient and accurate, as well as easier to use.

Application of a New Penalty Function Method to Design Optimization

This paper presents Schuldt’s Method of Multipliers for nonlinear programming problems. The basics of this new exterior penalty function method are discussed with emphasis upon the ease of implementation. The merit of the technique for medium to large non-linear programming problems is evaluated, and demonstrated using the Eason and Fenton test problems.

An Extension of Duality-Stability Relations to Nonconvex Optimization Problems

By an effective extension of the conjugate function concept a general framework for duality-stability relations in nonconvex optimization problems can be studied. The results obtained show strong correspondences with the duality theory for convex minimization problems. In specializations to mathematical programming problems the canonical Lagrangian of the model appears as the extended Lagrangian considered in exterior penalty function methods.

Geometry and resolution of duality gaps

AbstractIn this study we interpret the exterior penalty function method as a generalized lagrangian metliod which fills duality gaps in nonconvex problems. Geometry and resolution of these gaps from a duality point of view are highlighted.

An Historical Survey of Computational Methods in Optimal Control

The last twenty years have seen a great flourishing in optimal control theory. In this paper, we shall highlight some of the salient theoretical developments in the specific area of algorithms. The first algorithms for optimal control were aimed at unconstrained problems and were derived by using first and second variation methods of the calculus of variations. These methods have subsequently been recognized as gradient, Newton–Raphson, or Gauss–Newton methods in function space. A much more recent addition to the arsenal of unconstrained optimal control algorithms are several variations of conjugate gradient methods. At first, constrained optimal control problems could only be solved by exterior penalty function methods. Later algorithms specifically designed for constrained problems have appeared. Among these we find methods for solving the unconstrained linear quadratic regulator problem as well as certain constrained minimum time and minimum energy problems. Differential-dynamic programming was developed from dynamic programming considerations. The conditional gradient method, the gradient projection method and a couple of feasible directions methods were obtained as extensions or adaptations of related algorithms for finite-dimensional problems. Finally, the so-called $\varepsilon $-methods combine the Ritz method with penalty function techniques. Some of the recent work has dealt with discretization effects. This has led to the concept of well-posedness of a problem and to adaptive integration techniques.