Recent efforts in differentiable non-linear programming have been focused on interior point methods, akin to penalty and barrier algorithms. In this paper, we address the classical equality constrained program solved using the simple quadratic loss penalty function/algorithm. The suggestion to use extrapolations to track the differentiable trajectory associated with penalized subproblems goes b...

The purpose of this work was to investigate the utility of implicit integration methods for molecular dynamics (MD) simulation. Implicit methods were investigated in an attempt to address the bottleneck associated with short, stability-limited step size lengths available to the explicit methods currently in widespread use. Two implicit methods were compared to the current standard for time inte...

In this paper we consider the numerical solution of the algebraic Riccati equation using Newton's method. We propose an inexact variant which allows one control the number of the inner iterates used in an iterative solver for each Newton step. Conditions are given under which the monotonicity and global convergence result of Kleinman also hold for the inexact Newton iterates. Numerical results ...

This paper analyzes local convergence rates of primal-dual interior point methods for general nonlinearly constrained optimization problems. For this purpose, we first discuss modified Newton methods and modified quasi-Newton methods for solving a nonlinear system of equations, and show local and Qquadratic/Q-superlinear convergence of these methods. These methods are characterized by a perturb...

In previous work by Rueter et al., low frequency (10–750 kHz) ultrasound was shown to penetrate the lung, motivating its use as a nonionizing tomographic technique for pulmonary monitoring. Here, we present method regularized full waveform inversion low-frequency data. A novel structural similarity index metric (SSIM)-based regularization term is introduced that compares correlation of current ...

In this paper, we are concerned with the numerical solution of simplicial cone constrained convex quadratic optimization (SCQO) problems. A reformulation K.K.T optimality conditions SCQOs as an equivalent linear complementarity problem $\mathcal{P}$-matrix ($\mathcal{P}$-LCP) is considered. Then, a feasible full-Newton step interior-point algorithm (IPA) applied for solving SCQO via $\mathcal{P...

We construct a new harmonic family: dielectric flow solutions with maximal supersymmetry in eleven-dimensional supergravity. These solutions are asymptotically AdS4 ×S7, while in the infra-red the M2 branes are dielectrically polarized into M5 branes. These solutions are holographically dual to vacua of the mass deformed theory on M2 branes. They also provide an interesting insight on the super...

As mentioned before, the success of CASE relies on two noteworthy properties: the Sure Screening (SS) property and the Separable After Screening (SAS) property. In this section, we discuss the two properties in detail, and illustrate how these properties enable us to decompose the original regression problem to many small-size regression problems which can be fit separately. We then use these p...

I describe a modification to Shanks’ baby-step giant-step algorithm for computing the order n of an element g of a group G, assuming n is finite. My method has the advantage of being able to compute n quickly, which Shanks’ method fails to do when the order of G is infinite, unknown, or much larger than n. I describe the algorithm in detail. I also present the results of implementations of my a...