A Projected-Search Interior Method for Nonlinear Optimization

This paper concerns the formulation and analysis of a new interior method for general nonlinearly constrained optimization that combines a shifted primal-dual interior method with a projected-search method for bound-constrained optimization. The method involves the computation of an approximate Newton direction for a primal-dual penalty-barrier function that incorporates shifts on both the primal and dual … Read more

A Shifted Primal-Dual Interior Method for Nonlinear Optimization

Interior methods provide an effective approach for the treatment of inequality constraints in nonlinearly constrained optimization. A new primal-dual interior method is proposed based on minimizing a sequence of shifted primal-dual penalty-barrier functions. Certain global convergence properties are established. In particular, it is shown that every limit point is either an infeasible stationary point, or … Read more

Iterative Solution of Augmented Systems Arising in Interior Methods

Iterative methods are proposed for certain augmented systems of linear equations that arise in interior methods for general nonlinear optimization. Interior methods define a sequence of KKT equations that represent the symmetrized (but indefinite) equations associated with Newton’s method for a point satisfying the perturbed optimality conditions. These equations involve both the primal and dual … Read more

KNITRO-Direct: A Hybrid Interior Algorithm for Nonlinear Optimization

A hybrid interior-point method for nonlinear programming is presented. It enjoys the flexibility of switching between a line search based method which computes steps by factoring the primal-dual equations and an iterative method using a conjugate gradient algorithm and globalized by means of trust regions. Steps computed by a direct factorization are always tried first, … Read more

A Starting-Point Strategy for Nonlinear Interior Methods

This paper presents a strategy for choosing the initial point, slacks and multipliers in interior methods for nonlinear programming. It consists of first computing a Newton-like step to estimate the magnitude of these three variables and then shifting the slacks and multipliers so that they are sufficiently positive. The new strategy has the option of … Read more