A generally nonconvex optimization problem with equality constraints is studied. The problem is introduced as an “inf sup” of a generalized augmented Lagrangian function. A dual problem is defined as the “sup inf’ of the same generalized augmented Lagrangian. Sufftcient conditions are derived for constructing the augmented Lagrangian function such that the extremal values of the primal and dual...

Whereas CP methods are strong with respect to the detection of local infeasibilities, OR approaches have powerful optimization abilities that ground on tight global bounds on the objective. An integration of propagation ideas from CP and Lagrangian relaxation techniques from OR combines the merits of both approaches. We introduce a general way of how linear optimization constraints can strength...

We propose an augmented Lagrangian algorithm for solving large-scale equality constrained optimization problems. The novel feature of the algorithm is an adaptive update for the penalty parameter motivated by recently proposed techniques for exact penalty methods. This adaptive updating scheme greatly improves the overall performance of the algorithm without sacrificing the strengths of the cor...

a fundamental topic in computational fluid dynamics is the role of coordinate particularly for searching optimized coordinates. the objective of this study is the numerical modeling of supersonic flows using a new coordinate system i.e. unified coordinate system (ucs) uses moving mesh with motionless viewing window technique. ucs has an advantage over traditional coordinate systems (eulerian an...

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...

In this paper we study nonlinear Lagrangian functions for constrained optimization problems which are, in general, nonlinear with respect to the objective function. We establish an equivalence between two types of zero duality gap properties, which are described using augmented Lagrangian dual functions and nonlinear Lagrangian dual functions, respectively. Furthermore, we show the existence of...

In this paper, we aim at unifying, simplifying, and improving the convergence rate analysis of Lagrangian-based methods for convex optimization problems. We first introduce notion nice primal algorithmic map, which plays a central role in unification simplification most methods. Equipped with then versatile generic scheme, allows design faster Lagrangian (FLAG) new provably sublinear expressed ...