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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TL;DR: It is now realistic to solve NLPs on the order of a million variables, for instance, with the IPOPT algorithm, and the recent NLP sensitivity extension to IPopT quickly computes approximate solutions of perturbed NLPs, allowing on-line computations to be drastically reduced.
496 citations
27 Aug 2004
TL;DR: In this article, the idea of continuous designs for moving sensors is proposed to optimize sensor trajectories based on the optimal experimental design problem in the presence of correlated observations and maximizing an Observability Measure.
Abstract: INTRODUCTION The Optimum Experimental Design Problem in Context A General Overview of Literature KEY IDEAS OF IDENTIFICATION AND EXPERIMENTAL DESIGN System Description Parameter Identification Measurement Location Problem Main Impediments Deterministic Interpretation of the FIM Calculation of Sensitivity Coefficients A Final Introductory Note LOCALLY OPTIMAL DESIGNS FOR STATIONARY SENSORS Linear-in-Parameters Lumped Models Construction of Minimax Designs Continuous Designs in Measurement Optimization Clusterization-Free Designs Nonlinear Programming Approach A Critical Note on Some Deterministic Approach Modifications Required by Other Settings Summary LOCALLY OPTIMAL STRATEGIES FOR SCANNING AND MOVING OBSERVATIONS Optimal Activation Policies for Scanning Sensors Adapting the Idea of Continuous Designs for Moving Sensors Optimization of Sensor Trajectories Based on Optimal-Control Techniques Concluding Remarks MEASUREMENT STRATEGIES WITH ALTERNATIVE DESIGN OBJECTIVES Optimal Sensor Location for Prediction Sensor Location for Model Discrimination Conclusions ROBUST DESIGNS FOR SENSOR LOCATION Sequential Designs Optimal Designs in the Average Sense Optimal Designs in the Minimax Sense Robust Sensor Location Using Randomized Algorithms Concluding Remarks TOWARDS EVEN MORE CHALLENGING PROBLEMS Measurement Strategies in the Presence of Correlated Observations Maximization of an Observability Measure Summary APPLICATIONS FROM ENGINEERING Electrolytic Reactor Calibration of Smog Prediction Models Monitoring of Groundwater Resources Quality Diffusion Process With Correlated Observational Errors Vibrating H-Shaped Membrane CONCLUSIONS AND FUTURE RESEARCH DIRECTIONS APPENDICES List of Symbols Mathematical Background On Statistical Properties of Estimators Analysis of the Largest Eigenvalue Differentiation of Nonlinear Operators Accessory Results for PDE's Interpolation of Tabulated Sensitivity Coefficients Differentials of Section 4.3.3 Solving Sensor Location Problems Using Maple and MATLAB
494 citations
TL;DR: The bi-level linear case is addressed in detail and the reformulated optimization problem is linear save for a complementarity constraint of the form 〈u, g〉 = 0.
493 citations
TL;DR: A nonlinear optimization algorithm for solving the problem of phase retrieval with transverse translation diversity, where the diverse far-field intensity measurements are taken after translating the object relative to a known illumination pattern, achieves superior reconstructions.
Abstract: We develop and test a nonlinear optimization algorithm for solving the problem of phase retrieval with transverse translation diversity, where the diverse far-field intensity measurements are taken after translating the object relative to a known illumination pattern. Analytical expressions for the gradient of a squared-error metric with respect to the object, illumination and translations allow joint optimization of the object and system parameters. This approach achieves superior reconstructions, with respect to a previously reported technique [H. M. L. Faulkner and J. M. Rodenburg, Phys. Rev. Lett. 93, 023903 (2004)], when the system parameters are inaccurately known or in the presence of noise. Applicability of this method for samples that are smaller than the illumination pattern is explored.
491 citations
TL;DR: This work explicitly characterize the robust counterpart of a linear programming problem with uncertainty set described by an arbitrary norm as well as providing guarantees for constraint violation under probabilistic models that allow arbitrary dependencies in the distribution of the uncertain coefficients.
489 citations