Excessive deformations and chatter vibrations are two main obstacles frequently encountered in turning of long slender workpieces. So far, there is seldom reported research using optimization techniques to cope with those difficulties. This paper introduces a new method for optimizing the machining parameters and the sequence of cutting passes in turning of a slender rod to control the deformat...

The large volume principle proposed by Vladimir Vapnik, which advocates that hypotheses lying in an equivalence class with a larger volume are more preferable, is a useful alternative to the large margin principle. In this paper, we introduce a clustering model based on the large volume principle called maximum volume clustering (MVC), and propose two algorithms to solve it approximately: a sof...

In this paper, we consider a special class of nonlinear semi-definite programming problems that represents the fixed orderH 2/H∞ synthesis problem. An augmented Lagrangian sequential quadratic programming method combined with a trust region globalization strategy is described, taking advantage of the problem structure and using inexact computations. Some numerical examples that illustrate the p...

Quadratic programming (QP) is an optimization problem wherein one minimizes (or maximizes) a quadratic function of a finite number of decision variable subject to a finite number of linear inequality and/ or equality constraints. In this paper, a quadratic programming problem (FFQP) is considered in which all cost coefficients, constraints coefficients, and right hand side are characterized by ...

We show that recently developed interior point methods for quadratic programming and linear complementarity problems can be put to use in solving discrete-time optimal control problems, with general pointwise constraints on states and controls. We describe interior point algorithms for a discrete time linear-quadratic regulator problem with mixed state/control constraints, and show how it can b...

A sequential quadratic programming (SQP) method is presented that aims to overcome some of the drawbacks of contemporary SQP methods. It avoids the difficulties associated with indefinite quadratic programming subproblems by defining this subproblem to be always convex. The novel feature of the approach is the addition of an equality constrained phase that promotes fast convergence and improves...

This paper studies Newton-type methods for minimization of partly smooth convex functions. Sequential Newton methods are provided using local parameterizations obtained from U-Lagrangian theory and from Riemannian geometry. The Hessian based on the ULagrangian depends on the selection of a dual parameter g; by revealing the connection to Riemannian geometry, a natural choice of g emerges for wh...

We show that the quadratic growth condition and the Mangasarian-Fromovitz constraint qualiication imply that local minima of nonlinear programs are isolated stationary points. As a result, when started suuciently close to such points, an L1 exact penalty sequential quadratic programming algorithm will induce at least R-linear convergence of the iterates to such a local minimum. We construct an ...

This paper concerns some practical issues associated with the formulation of sequential quadratic programming (SQP) methods for large-scale nonlinear optimization. SQP methods find an approximate solution of a sequence of quadratic programming (QP) subproblems in which a quadratic model of the objective function is minimized subject to the linearized constraints. Extensive numerical results are...

A natural damping of Newton's method for nonsmooth equations is presented. This damping, via the path search instead of the traditional line search, enlarges the domain of convergence of Newton's method and therefore is said to be globally convergent. Convergence behavior is like that of line search damped Newton's method for smooth equations, including Q-quadratic convergence rates under appro...