Primal-dualinterior-point methods have proven to be very successful for both linear programming (LP) and, more recently, for semideenite programming (SDP) problems. Many of the techniques that have been so successful for LP have been extended to SDP. In fact, interior point methods are currently the only successful techniques for SDP. We present a new paradigm for deriving these methods: 1) usi...

In this paper, we apply the alternating direction method (ADM) to solve a constrained linear least-squares problem where the objective function is a sum of two least-squares terms and the constraints are box constraints. Using ADM, we decompose the original problem into two easier least-squares subproblems at each iteration. To speed up the inner iteration, we linearize the subproblems whenever...

It has been known since the early 1970s that the Hessian matrices in quasi– Newton methods can be updated by variational means, in several different ways. The usual formulation of these variational problems uses a coordinate system, and the symmetry of the Hessian matrices are enforced as explicit constraints. As a result, the variational problems seem complicated. In this paper, we give a very...

Constrained least squares estimation lies at the heart of many applications in fields as diverse as statistics, psychometrics, signal processing, or even machine learning. Nonnegativity requirements on the model variables are amongst the simplest constraints that arise naturally, and the corresponding least-squares problem is called Nonnegative Least Squares or NNLS. In this paper we present a ...

The power systems state estimation problem computes the set of complex voltage phasors given quadratic measurements using nonlinear least squares (NLS). This is a nonconvex optimization problem, so even in the absence of measurement errors, local search algorithms like Newton / Gauss–Newton can become “stuck” at local minima, which correspond to nonsensical estimations. In this paper, we observ...

The power systems state estimation problem computes the set of complex voltage phasors given quadratic measurements using nonlinear least squares (NLS). This is a nonconvex optimization problem, so even in the absence of measurement errors, local search algorithms like Newton / Gauss–Newton can become “stuck” at local minima, which correspond to nonsensical estimations. In this paper, we observ...

A new optimization formulation for simulating multiphase flow in porous media is introduced. A locally mass-conservative, mixed finite-element method is employed for the spatial discretization. An unconditionally stable, fully-implicit time discretization is used and leads to a coupled system of nonlinear equations that must be solved at each time step. We reformulate this system as a least squ...

This paper investigates the use of statistical linearization to improve iterative non-linear least squares estimators. In particular, we look at improving long range stereo by filtering feature tracks from sequences of stereo pairs. A novel filter called the Iterated Sigma Point Kalman Filter (ISPKF) is developed from first principles; this filter is shown to achieve superior performance in ter...

To prove that a polynomial is nonnegative on Rn one can try to show that it is a sum of squares of polynomials. The latter problem is now known to be reducible to a semidefinite programming computation much faster than classical algebraic methods, thus enabling new speed-ups in algebraic optimization. However, exactly how often nonnegative polynomials are in fact sums of squares of polynomials ...

We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on discrepancy principle. formulate problem as an equality constrained optimization problem, where constraint is given by least squares data fidelity term and expresses The objective function convex that incorporates some prior knowledge, such total variation function. Using Jac...