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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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Journal ArticleDOI
TL;DR: In this paper, the authors give a brief overview of important results in several areas of sensitivity and stability analysis for nonlinear programming, focusing initially on qualitative characterizations (e.g., continuity, differentiability and convexity) of the optimal value function.
Abstract: We give a brief overview of important results in several areas of sensitivity and stability analysis for nonlinear programming, focusing initially on “qualitative” characterizations (e.g., continuity, differentiability and convexity) of the optimal value function. Subsequent results concern “quantitative” measures, in particular optimal value and solution point parameter derivative calculations, algorithmic approximations, and bounds. Our treatment is far from exhaustive and concentrates on results that hold for smooth well-structured problems.

141 citations

Journal ArticleDOI
TL;DR: A new nonlinear integer programming representation of the static channel assignment (SCA) problem is formulated and a new self-organizing neural network is proposed which is able to solve the SCA problem and many other practical optimization problems due to its generalizing ability.
Abstract: We examine the problem of assigning calls in a cellular mobile network to channels in the frequency domain. Such assignments must be made so that interference between calls is minimized, while demands for channels are satisfied. A new nonlinear integer programming representation of the static channel assignment (SCA) problem is formulated. We then propose two different neural networks for solving this problem. The first is an improved Hopfield (1982) neural network which resolves the issues of infeasibility and poor solution quality which have plagued the reputation of the Hopfield network. The second approach is a new self-organizing neural network which is able to solve the SCA problem and many other practical optimization problems due to its generalizing ability. A variety of test problems are used to compare the performance of the neural techniques against more traditional heuristic approaches. Finally, extensions to the dynamic channel assignment problem are considered.

141 citations

Journal ArticleDOI
TL;DR: While almost all existing nonmetric distortion calibration methods needs user involvement in one form or another, this paper presents a robust approach based on the least-median-of-squares estimator, able to proceed in a fully automatic manner while being less sensitive to erroneous input data such as image curves that are mistakenly considered projections of three-dimensional linear segments.
Abstract: This paper addresses the problem of calibrating camera lens distortion, which can be significant in medium to wide angle lenses. Our approach is based on the analysis of distorted images of straight lines. We derive new distortion measures that can be optimized using nonlinear search techniques to find the best distortion parameters that straighten these lines. Unlike the other existing approaches, we also provide fast, closed-form solutions to the distortion coefficients. We prove that including both the distortion center and the decentering coefficients in the nonlinear optimization step may lead to instability of the estimation algorithm. Our approach provides a way to get around this, and, at the same time, it reduces the search space of the calibration problem without sacrificing the accuracy and produces more stable and noise-robust results. In addition, while almost all existing nonmetric distortion calibration methods needs user involvement in one form or another, we present a robust approach to distortion calibration based on the least-median-of-squares estimator. Our approach is, thus, able to proceed in a fully automatic manner while being less sensitive to erroneous input data such as image curves that are mistakenly considered projections of three-dimensional linear segments. Experiments to evaluate the performance of this approach on synthetic and real data are reported.

141 citations

Book ChapterDOI
26 Mar 2011
TL;DR: Using a new version of parametric probabilistic model checking, it is shown how the Model Repair problem can be reduced to a nonlinear optimization problem with a minimal-cost objective function, thereby yielding a solution technique.
Abstract: We introduce the problem of Model Repair for Probabilistic Systems as follows Given a probabilistic system M and a probabilistic temporal logic formula φ such that M fails to satisfy φ, the Model Repair problem is to find an M′ that satisfies v and differs from M only in the transition flows of those states in M that are deemed controllable Moreover, the cost associated with modifying M's transition flows to obtain M′ should be minimized Using a new version of parametric probabilistic model checking, we show how the Model Repair problem can be reduced to a nonlinear optimization problem with a minimal-cost objective function, thereby yielding a solution technique We demonstrate the practical utility of our approach by applying it to a number of significant case studies, including a DTMC reward model of the Zeroconf protocol for assigning IP addresses, and a CTMC model of the highly publicized Kaminsky DNS cache-poisoning attack

140 citations

Journal ArticleDOI
TL;DR: The application of the transcription method is described to compute an optimal low thrust transfer from an Earth orbit using a sparse nonlinear programming algorithm with a discretization of the trajectory dynamics.
Abstract: The direct transcription or collocation method has demonstrated notable success in the solution of trajectory optimization and optimal control problems. This approach combines a sparse nonlinear programming algorithm with a discretization of the trajectory dynamics. A challenging class of optimization problems occurs when the spacecraft trajectories are characterized by thrust levels that are very low relative to the vehicle weight. Low thrust trajectories are demanding because realistic forces, due to oblateness, and third-body perturbations often dominate the thrust. Furthermore, because the thrust is so low, significant changes to the orbits require very long duration trajectories. When a collocation method is applied to a problem of this type, the resulting nonlinear program is very large, because the trajectories are long, and very nonlinear because of the perturbing forces.This paper describes the application of the transcription method to compute an optimal low thrust transfer from an Earth orbit t...

140 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023113
2022259
2021615
2020650
2019640
2018630