Two interior-point algorithms are proposed and analyzed, for the (local) solution of (possibly) indefinite quadratic programming problems. They are of the Newton-KKT variety in that (much like in the case of primal-dual algorithms for linear programming) search directions for the “primal” variables and the Karush-Kuhn-Tucker (KKT) multiplier estimates are components of the Newton (or quasi-Newt...

In this paper, we investigate the use of an exact primal-dual penalty approach within the framework of an interior-point method for nonconvex nonlinear programming. This approach provides regularization and relaxation, which can aid in solving ill-behaved problems and in warmstarting the algorithm. We present details of our implementation within the loqo algorithm and provide extensive numerica...

1 The authors would like to thank two anonymous referees for their helpful suggestions leading to a improved presentation of the paper. Abstract. Two interior-point algorithms using a wide neighborhood of the central path are proposed to solve nonlinear P-complementarity problems. The proof of the polynomial complexity of the rst method requires that the problem satisses a scaled Lipschitz cond...

This paper deals with an algorithm which incorporates the interior point method into the Dantzig-Wolfe decomposition technique for solving large-scale linear programming problems. At each iteration, the algorithm performs one step of Newton's method to solve a subproblem, obtaining an approximate solution, which is then used to compute an approximate Newton direction to nd a new vector of the L...

In this paper we continue the development of a theoretical foundation for efficient primal-dual interior-point algorithms for convex programming problems expressed in conic form, when the cone and its associated barrier are self-scaled (see [NT97]). The class of problems under consideration includes linear programming, semidefinite programming and convex quadratically constrained quadratic prog...

In this paper, we present the formulation and solution of optimization problems with complementarity constraints using an interior-point method for nonconvex nonlinear programming. We identify possible difficulties that could arise, such as unbounded faces of dual variables, linear dependence of constraint gradients and initialization issues. We suggest remedies. We include encouraging numerica...

Hyperbolic polynomials have their origins in partial diierential equations. We show in this paper that they have applications in interior point methods for convex programming. Each homogeneous hyperbolic polynomial p has an associated open and convex cone called its hyperbolicity cone. We give an explicit representation of this cone in terms of polynomial inequalities. The function F (x) = ? lo...

This paper describes a novel approach to recovering a parametric deformation that optimally registers one image to another. The method proceeds by constructing a global convex approximation to the match function which can be optimized using interior point methods. The paper also describes how one can exploit the structure of the resulting optimization problem to develop efficient and effective ...

Some Jordan algebras were proved more than a decade ago to be an indispensable tool in the unified study of interior-point methods. By using it, we generalize the infeasible interiorpoint method for linear optimization of Roos [SIAM J. Optim., 16(4):1110–1136 (electronic), 2006] to symmetric optimization. This unifies the analysis for linear, second-order cone and semidefinite optimizations.

In most primal-dual interior point methods, a sequence of weighted normal equations are solved, where the only change from one problem to the next are the weights and the right hand side. Solving the normal equations alternating between a direct method and an iterative method was introduced in Wang and O'Leary 11]. A class of preconditioners based on a low-rank correction of a Cholesky factoriz...