Topic
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.
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01 Dec 2010
TL;DR: Under mild conditions the local convergence of the algorithm is proved as a main result of this paper, and an application to optimal control illustrates the performance of the proposed algorithm.
Abstract: This paper introduces sequential convex programming (SCP), a local optimzation method for solving nonconvex optimization problems. A full-step SCP algorithm is presented. Under mild conditions the local convergence of the algorithm is proved as a main result of this paper. An application to optimal control illustrates the performance of the proposed algorithm.
154 citations
TL;DR: A new algorithm, ordered subsets mirror descent, is developed and implemented, and it is demonstrated that it is well suited for solving the PET reconstruction problem.
Abstract: We describe an optimization problem arising in reconstructing three-dimensional medical images from positron emission tomography (PET). A mathematical model of the problem, based on the maximum likelihood principle, is posed as a problem of minimizing a convex function of several million variables over the standard simplex. To solve a problem of these characteristics, we develop and implement a new algorithm, ordered subsets mirror descent, and demonstrate, theoretically and computationally, that it is well suited for solving the PET reconstruction problem.
154 citations
01 Jan 1991
TL;DR: This paper explores and reviews control techniques based on repeated solution of nonlinear programming (NLP) problems and presents a basic algorithm for optimization-based process control, a straightforward extension of popular model-predictive controllers that are used for linear systems.
Abstract: With the development of sophisticated methods for nonlinear programming and powerful computer hardware, it now becomes useful and efficient to formulate and solve nonlinear process control problems through on-line optimization methods This paper explores and reviews control techniques based on repeated solution of nonlinear programming (NLP) problems Here several advantages present themselves These include minimization of readily quantifiable objectives, coordinated and accurate handling of process nonlinearities and interactions, and systematic ways of dealing with process constraints We motivate this NLP-based approach with small nonlinear examples and present a basic algorithm for optimization-based process control As can be seen this approach is a straightforward extension of popular model-predictive controllers (MPCs) that are used for linear systems The statement of the basic algorithm raises a number of questions regarding stability and robustness of the method, efficiency of the control calculations, incorporation of feedback into the controller and reliable ways of handling process constraints Each of these will be treated through analysis and/or modification of the basic algorithm To highlight and support this discussion, several examples are presented and key results are examined and further developed 74 refs, 11 figs
154 citations
TL;DR: An optimization model with a nonlinear objective function subject to a system of fuzzy relation equations is presented and a genetic algorithm is proposed designed to be domain specific by taking advantage of the structure of the solution set of fuzzy relationship equations.
153 citations
TL;DR: It was indicated that the proposed linearization method was effective in dealing with IFNP problems; uncertainties can be communicated into optimization process and generate reliable solutions for decision variables and objectives; the decision alternatives can be obtained by adjusting different combinations of the decision variables within their solution intervals.
153 citations