This paper describes an approach to reformulating the stereo matching problem as a large scale Linear Program. The approach proceeds by approximating the match cost function associated with each pixel with a piecewise linear convex function. Regularization terms related to the first and second derivative of the disparity field are also captured with piecewise linear penalty terms. The resulting...

Trajectory optimization is an important means to improve performance in many industrial and scientiic processes such as robotics or aerospace applications. A combination of SQP methods with direct collocation or multiple shooting discretizations has proven very successful for such problems. In realistic applications, however, very large QP sub-problems with thousands of constraints may arise. T...

We investigate the use of interior-point methods for solving quadratic programming problems with a small number of linear constraints, where the quadratic term consists of a low-rank update to a positive semidefinite matrix. Several formulations of the support vector machine fit into this category. An interesting feature of these particular problems is the volume of data, which can lead to quad...

Hopfield neural networks and interior point methods are used in an integrated way to solve linear optimization problems. The Hopfield network gives warm start for the primal–dual interior point methods, which can be way ahead in the path to optimality. The approaches were applied to a set of real world linear programming problems. The integrated approaches provide promising results, indicating ...

We study the situation in which, having solved a linear program with an interiorpoint method, we are presented with a new problem instance whose data is slightly perturbed from the original. We describe strategies for recovering a \warm-start" point for the perturbed problem instance from the iterates of the original problem instance. We obtain worst-case estimates of the number of iterations r...

This paper proposes a new predictor-corrector interior-point method for a class of semidefinite programs, which numerically traces the central trajectory in a space of Lagrange multipliers. The distinguished features of the method are full use of the BFGS quasi-Newton method in the corrector procedure, and an application of the conjugate gradient method with an effective preconditioning matrix ...

A new class of preconditioners is proposed for the iterative solution of symmetric indefinite systems arising from interior-point methods. The use of logarithmic barriers in interior point methods causes unavoidable ill-conditioning of linear systems and, hence, iterative methods fail to provide sufficient accuracy unless appropriately preconditioned. Now we introduce two types of preconditione...

Primal-dual interior-point methods for linear complementarity and linear programming problems solve a linear system of equations to obtain a modiied Newton step at each iteration. These linear systems become increasingly ill-conditioned in the later stages of the algorithm, but the computed steps are often suuciently accurate to be useful. We use error analysis techniques tailored to the specia...

In the conic formulation of a convex optimization problem the constraints are expressed as linear inequalities with respect to a possibly non-polyhedral convex cone. This makes it possible to formulate elegant extensions of interior-point methods for linear programming to general nonlinear convex optimization. Recent research on cone programming algorithms has particularly focused on three conv...