Nonlinear programming

About: Nonlinear programming is a research topic. Over the lifetime, 19486 publications have been published within this topic receiving 656602 citations. The topic is also known as: non-linear programming & NLP.

Mesh refinement in direct transcription methods for optimal control

Abstract: SUMMARY The direct transcription method for solving optimal control problems involves the use of a discrete approximation to the original problem. This paper describes a technique for changing the discretization in order to improve the accuracy of the approximation. An integer programming technique is used to minimize the maximum error during the refinement iterations. The eƒciency of the method is illustrated for an application with path inequality constraints. ( 1998 John Wiley & Sons, Ltd.

Nonlinear Chance-Constrained Process Optimization under Uncertainty

Abstract: Optimization under uncertainty is considered necessary for robust process design and operation. In this work, a new approach is proposed to solve a kind of nonlinear optimization problem under uncertainty, in which some dependent variables are to be constrained with a predefined probability. Such problems are called optimization under chance constraints. By employment of the monotony of these variables to one of the uncertain variables, the output feasible region will be mapped to a region of the uncertain input variables. Thus, the probability of holding the output constraints can be simply achieved by integration of the probability density function of the multivariate uncertain variables. Collocation on finite elements is used for the numerical integration, through which sensitivities of the chance constraints can be computed as well. The proposed approach is applied to the optimization of two process engineering problems under various uncertainties.

Fuzzy model predictive control

Abstract: A fuzzy model predictive control (FMPC) approach is introduced to design a control system for a highly nonlinear process. In this approach, a process system is described by a fuzzy convolution model that consists of a number of quasi-linear fuzzy implications. In controller design, prediction errors and control energy are minimized through a two-layered iterative optimization process. At the lower layer, optimal local control policies are identified to minimize prediction errors in each subsystem. A near optimum is then identified through coordinating the subsystems to reach an overall minimum prediction error at the upper layer. The two-layered computing scheme avoids extensive online nonlinear optimization and permits the design of a controller based on linear control theory. The efficacy of the FMPC approach is demonstrated through three examples.

Simultaneous cyclic scheduling and control of a multiproduct CSTR

Abstract: In this work, we propose a simultaneous scheduling and control formulation by explicitly incorporating into the scheduling model process dynamics in the form of differential/algebraic constraints. The formulation takes into account the interactions between scheduling and control and is able to handle nonlinearities embedded into the processing system. The simultaneous scheduling and control problems is cast as a mixed-integer dynamic optimization (MIDO) problem where the simultaneous approach, based on orthogonal collocation on finite elements, is used to transform it into a mixed-integer nonlinear programming (MINLP) problem. The proposed simultaneous scheduling and control formulation is tested using three multiproduct continuous stirred tank reactors featuring difficult nonlinearities.

Inexact Newton methods for the nonlinear complementarity problem

Abstract: An exact Newton method for solving a nonlinear complementarity problem consists of solving a sequence of linear complementarity subproblems. For problems of large size, solving the subproblems exactly can be very expensive. In this paper we study inexact Newton methods for solving the nonlinear, complementarity problem. In such an inexact method, the subproblems are solved only up to a certain degree of accuracy. The necessary accuracies that are needed to preserve the nice features of the exact Newton method are established and analyzed. We also discuss some extensions as well as an application.