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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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TL;DR: Improvements are introduced including mutations to the nonlinear simplex method to search around the boundary of the feasible region and to control the convergence speed of the method, the /spl alpha/ constrained method is applied and the improved /splalpha/ constrainedsimplex method is proposed for constrained optimization problems.
Abstract: Constrained optimization problems are very important and frequently appear in the real world. The /spl alpha/ constrained method is a new transformation method for constrained optimization. In this method, a satisfaction level for the constraints is introduced, which indicates how well a search point satisfies the constraints. The /spl alpha/ level comparison, which compares search points based on their level of satisfaction of the constraints, is also introduced. The /spl alpha/ constrained method can convert an algorithm for unconstrained problems into an algorithm for constrained problems by replacing ordinary comparisons with the /spl alpha/ level comparisons. In this paper, we introduce some improvements including mutations to the nonlinear simplex method to search around the boundary of the feasible region and to control the convergence speed of the method, we apply the /spl alpha/ constrained method and we propose the improved /spl alpha/ constrained simplex method for constrained optimization problems. The effectiveness of the /spl alpha/ constrained simplex method is shown by comparing its performance with that of the stochastic ranking method on various constrained problems.

160 citations

Journal ArticleDOI
TL;DR: TIMP is an R package for modeling multiway spectroscopic measurements that fits separable nonlinear models using partitioned variable projection, a variant of the variable projection algorithm that is described here for the first time.
Abstract: TIMP is an R package for modeling multiway spectroscopic measurements. The package allows for the simultaneous analysis of datasets collected under different experimental conditions in terms of a wide variety of parametric models. Models arising in spectroscopy data analysis often have some parameters that are intrinstically nonlinear, and some parameters that are conditionally linear on estimates of the nonlinear parameters. TIMP fits such separable nonlinear models using partitioned variable projection, a variant of the variable projection algorithm that is described here for the first time. The of the partitioned variable projection algorithm allows fitting many models for spectroscopy datasets using much less memory as compared to under the standard variable projection algorithm that is implemented in nonlinear optimization routines (e.g., the plinear option of the R function nls), as is shown here. An overview of modeling with TIMP is also given that includes several case studies in the application of the package.

159 citations

Journal ArticleDOI
TL;DR: Two new versions of the controlled random search procedure for global optimization (CRS) are described, intended to drive an optimizing accelerator, based on a concurrent processing architecture, which can be attached to a workstation to achieve a significant increase in speed.
Abstract: This paper describes two new versions of the controlled random search procedure for global optimization (CRS). Designed primarily to suit the user of a CAD workstation, these algorithms can also be used effectively in other contexts. The first, known as CRS3, speeds the final convergence of the optimization by combining a local optimization algorithm with the global search procedure. The second, called CCRS, is a concurrent version of CRS3. This algorithm is intended to drive an optimizing accelerator, based on a concurrent processing architecture, which can be attached to a workstation to achieve a significant increase in speed. The results are given of comparative trials which involve both unconstrained and constrained optimization.

159 citations

Journal ArticleDOI
TL;DR: Two new trust-region methods for solving nonlinear optimization problems over convex feasible domains are presented, distinguished by the fact that they do not enforce strict monotonicity of the objective function values at successive iterates.
Abstract: This paper presents two new trust-region methods for solving nonlinear optimization problems over convex feasible domains. These methods are distinguished by the fact that they do not enforce strict monotonicity of the objective function values at successive iterates. The algorithms are proved to be convergent to critical points of the problem from any starting point. Extensive numerical experiments show that this approach is competitive with the LANCELOT package.

159 citations

Journal ArticleDOI
TL;DR: In this paper, a general low-thrust trade analysis tool is developed based on a global search for local indirect method solutions, and an efficient propagator is implemented with an implicit "bang-bang" thrusting structure with an a priori unknown number of switching times.
Abstract: The low-thrust spacecraft trajectory problem can be reduced to only a few parameters using calculus of variations and the well-known primer vector theory. This low dimensionality combined with the extraordinary speed of modern computers allows for rapid exploration of the parameter space and invites opportunities for global optimization. Accordingly, a general low-thrust trade analysis tool is developed based on a global search for local indirect method solutions. An efficient propagator is implemented with an implicit "bang-bang" thrusting structure that accommodates an a priori unknown number of switching times. An extension to the standard adjoint control transformation is introduced that provides additional physical insight and control over the anticipated evolution of the thrust profile. The uniformly random search enjoys a perfect linear speedup for parallel implementation. The method is applied specifically on multi revolution transfers in the Jupiter-Europa and Earth-moon restricted three body problems. In both cases, thousands of solutions are found in a single parallel run. The result is a global front of Pareto optimal solutions across the competing objectives of flight time and final mass.

159 citations


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