This is a documentation of a framework for robotmotion optimization that aims to draw on classical constrained optimization methods. With one exception the underlying algorithms are classical ones: Gauss-Newton (with adaptive stepsize and damping), Augmented Lagrangian, log-barrier, etc. The exception is a novel any-time version of the Augmented Lagrangian. The contribution of this framework is...

Designing large-scale systems frequently involves solving a complex mathematical program that requires, for various reasons, decomposition into a number of smaller systems. Practical studies have proved the effectiveness of multilevel hierarchical methods at early stages of design; these methods divide a large program into multiple levels and multiple systems at each level and the result is kno...

Based on the classic augmented Lagrangian multiplier method, we propose, analyze and test an algorithm for solving a class of equality-constrained nonsmooth optimization problems (chiefly but not necessarily convex programs) with a particular structure. The algorithm effectively combines an alternating direction technique with a nonmonotone line search to minimize the augmented Lagrangian funct...

The aim of this work is to propose a new numerical method for solving the mechanical frictional contact problem in the general case of multi-bodies in a three dimensional space. This method is called adapted augmented Lagrangian method (AALM) and can be used in a multi-physical context (like thermo-electro-mechanical fields problems). This paper presents this new method and its advantages over ...

Sometimes, the feasible set of an optimization problem that one aims to solve using a Nonlinear Programming algorithm is empty. In this case, two characteristics of the algorithm are desirable. On the one hand, the algorithm should converge to a minimizer of some infeasibility measure. On the other hand, one may wish to find a point with minimal infeasibility for which some optimality condition...

We provide a simplified form of Primal Augmented Lagrange Multiplier algorithm. We intend to fill the gap in the steps involved in the mathematical derivations of the algorithm so that an insight into the algorithm is made. The experiment is focused to show the reconstruction done using this algorithm. Keywords-compressive sensing; l1-minimization; sparsity; coherence I.INTRODUCTION Compressive...

We consider minimization of the sum of a large number of convex functions, and we propose an incremental aggregated version of the proximal algorithm, which bears similarity to the incremental aggregated gradient and subgradient methods that have received a lot of recent attention. Under cost function differentiability and strong convexity assumptions, we show linear convergence for a sufficien...

A parallel-in-time algorithm based on an augmented Lagrangian approach is proposed to solve four-dimensional variational (4D-Var) data assimilation problems. The assimilation window is divided into multiple sub-intervals that allows to parallelize cost function and gradient computations. Solution continuity equations across interval boundaries are added as constraints. The augmented Lagrangian ...

This paper presents an augmented Lagrangian algorithm to solve continuous constrained global optimization problems. The algorithm approximately solves a sequence of bound constrained subproblems whose objective function penalizes equality and inequality constraints violation and depends on the Lagrange multiplier vectors and a penalty parameter. Each subproblem is solved by a population-based m...

Estimation of coeecients of partial diierential equations is ill-posed. Output-least-squares method is often used in practice. Convergence of the commonly used minimization algorithms for the inverse problem is often very slow. By using the augmented Lagrangian method, the inverse problem is reduced to a coupled linear algebraic system, which can be solved eeciently. Total variation techniques ...