A Reduced Hessian Method for Large-Scale Constrained Optimization

This paper investigates application of SQP optimization algorithms to nonlinear model predictive control. It considers feasible vs. infeasible path methods, sequential vs. simultaneous methods and reduced vs. full space methods. A new optimization algorithm coined rFOPT which remains feasibile with respect to inequality constraints is introduced. The suitable choices between these various strategies are assessed informally through a small CSTR case study. The case study also considers the effect various discretization methods have on the optimization problem.

show abstract

“…The first uses a sequential approach, see e.g. [10], while the second follows the simultaneous null-space approach [21], [22].…”

Section: Reduced Gradient Methodsmentioning

confidence: 99%

“…L and U are lower and upper bounds on z, and ftol is the feasibility tolerance for the nonlinear inequalities. The update rule for ζ k is given by [22]. The reduced Hessian approximation B k is updated by a BFGS scheme.…”

Section: Nonlinear Inequality Constraintsmentioning

confidence: 99%

A new optimization algorithm with application to nonlinear MPC

Martinsen

Biegler

Foss

2004

Journal of Process Control

Self Cite

View full text Add to dashboard Cite

show abstract

“…3. Reduced-gradient methods, described in References [11,24,25], for example. Variants that use second-order information are based on a reduced Hessian matrix (e.g.…”

Section: Inequality Constraints Arising From the Non-penetration Condmentioning

confidence: 99%

Algorithms for the analysis of 3D finite strain contact problems

Areias

Sá

Curnis

2004

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYFrom the constraint imposition aspects in 3D to friction regularization, various ideas are exposed in this paper. A variation of the Rockafellar Lagrangian is proposed which results in continuous second-order derivatives if Lagrange multiplier estimates are greater or equal than one. This fact allows the adoption of a full second-order (i.e. Lagrange-Newton) method avoiding sequential unconstrained minimization techniques. An algorithm for global and local contact detection is presented which is developed for dealing with large step sizes typical of implicit methods. A modified constraint definition to deal with non-smooth situations is presented. Aspects of friction implementation, including a regularization scheme which ensures stepwise objectivity, are detailed. Finally, several illustrative examples are carried out with success.

show abstract

“…Since (16) has just 1 degree of freedom (g), consider the iterative solution of (16) in the context of a reduced Hessian SQP framework [3]. Linearization of the constraints give:…”

Section: Interior Point Sqpmentioning

confidence: 99%