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An interior-point method for nonlinear programming is presented. It enjoys the flexibility of switching between a line search method that computes steps by factoring the primal-dual equations and a trust region method that uses a conjugate gradient iteration. Steps computed by direct factorization are always tried first, but if they are deemed ineffective,… (More)

This paper describes an active-set algorithm for large-scale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza [10]. The step computation is performed in two stages. In the first stage a linear program is solved to estimate the active set at the solution. The linear program is obtained by… (More)

This paper considers strategies for selecting the barrier parameter at every iteration of an interior-point method for nonlinear programming. Numerical experiments suggest that adaptive choices, such as Mehrotra's probing procedure, outperform static strategies that hold the barrier parameter fixed until a barrier optimality test is satisfied. A new… (More)

The global convergence properties of a class of penalty methods for nonlinear programming are analyzed. These methods include successive linear programming approaches , and more specifically, the successive linear-quadratic programming approach presented by Byrd, Gould, Nocedal and Waltz (Math. Programming 100(1):27–48, 2004). Every iteration requires the… (More)

A slack-based feasible interior point method is described which can be derived as a modiication of infeasible methods. The modiication is minor for most line search methods, but trust region methods require special attention. It is shown how the Cauchy point, which is often computed in trust region methods, must be modiied so that the feasible method is… (More)

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… (More)

This paper describes an active-set algorithm for nonlinear programming that solves a parametric linear programming subproblem at each iteration to generate an estimate of the active set. A step is then computed by solving an equality constrained quadratic program based on this active-set estimate. This approach respresents an extension of the standard… (More)

This paper presents an active-set algorithm for large-scale optimization that occupies the middle ground between sequential quadratic programming (SQP) and sequential linear-quadratic programming (SL-QP) methods. It consists of two phases. The algorithm first minimizes a piecewise linear approximation of the Lagrangian, subject to a linearization of the… (More)

This papers studies the performance of several interior-point and active-set methods on bound constrained optimization problems. The numerical tests show that the sequential linear-quadratic programming (SLQP) method is robust, but is not as effective as gradient projection at identifying the optimal active set. Interior-point methods are robust and require… (More)

This paper describes interior point methods for nonlinear programming endowed with infeasibility detection capabilities. The methods are composed of two phases, a main phase whose goal is to seek optimality, and a feasibility phase that aims exclusively at improving feasibility. A common characteristic of the algorithms is the use of a step-decomposition… (More)

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