Regularized and stabilized sequential quadratic programming methods are two classes of sequential quadratic programming (SQP) methods designed to resolve the numerical and theoretical difficulties associated with ill-posed or degenerate nonlinear optimization problems. Recently, a regularized SQP method has been proposed that provides a strong connection between augmented Lagrangian methods and...

We present a new particle tracking algorithm for accurately resolving large deformation and rotational motion fields, which takes advantage of both local global algorithms. call this method ScalE Rotation Invariant Augmented Lagrangian Particle Tracking (SerialTrack). This builds an iterative scale rotation invariant topology-based feature vector each within multi-scale algorithm. The kinematic...

In this study, the performance of the modified subgradient algorithm (MSG) to solve the 0-1 quadratic knapsack problem (QKP) is examined. The MSG is proposed by Gasimov for solving dual problems constructed with respect to sharp Augmented Lagrangian function. The MSG has some important proven properties. For example, it is convergent, and it guarantees the zero duality gap for the problems such...

When designing robust controllers, H-in nity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These...

In this work we introduce a relaxed version of the constant positive linear dependence constraint qualification (CPLD) that we call RCPLD. This development is inspired by a recent generalization of the constant rank constraint qualification from Minchenko and Stakhovski that was called RCR. We show that RCPLD is enough to ensure the convergence of an augmented Lagrangian algorithm and asserts t...

Early work in augmented reality grew out of virtual reality research domains. These initial augmented reality systems applied the same methods and technology to solve what at first appeared to be a similar problem: correctly render a scene of virtual objects as the user changes viewpoint in the world. This is indeed similar for augmented and virtual reality systems. In virtual reality systems o...

We present in this paper an iterative algorithm to solve constraint forces for haptic interactive simulation. The haptic forces are induced by interaction with guidance virtual fixtures having forbidden regions. In general, a haptic rendering based on an explicit formulation of the constraint forces (with virtual springs) can lead to severe numerical stability problems in case of hard constrain...

We consider the task of design optimization, where the constraint is a state equation that can only be solved by a typically rather slowly converging fixed point solver. This process can be augmented by a corresponding adjoint solver, and based on the resulting approximate reduced derivatives, also an optimization iteration, which actually changes the design. To coordinate the three iterative p...

Methodologies to analyze error recovery properties of Variable Length Codes (VLCs) have been introduced in [1] and [2]. In this paper, we extend these methods to analyze the error-resilience of VLCs when soft decoding with length constraint strategies are applied at the decoder side. The approach allows in particular to compute the amount of information conveyed by the length constraint on a tr...

We introduce a filter mechanism to force convergence for augmented Lagrangian methods for nonlinear programming. In contrast to traditional augmented Lagrangian methods, our approach does not require the use of forcing sequences that drive the first-order error to zero. Instead, we employ a filter to drive the optimality measures to zero. Our algorithm is flexible in the sense that it allows fo...