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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.


Papers
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Journal ArticleDOI
TL;DR: In this article, a multi-period nonlinear programming model for the production planning and product distribution of several continuous multiproduct plants that are located in different sites and supply different markets is proposed.
Abstract: In this paper we propose a multiperiod nonlinear programming model for the production planning and product distribution of several continuous multiproduct plants that are located in different sites and supply different markets. The unique feature of the proposed model is that each plant is represented through nonlinear process models. To solve the resulting large-scale model, we present two solution techniques based on Lagrangean decomposition. Spatial decomposition is based on the idea of dualizing interconnection constraints between the plants and markets in order to be able to optimize each site and market individually. For the temporal decomposition, the interconnection constraints are defined between each time period through the inventory variables so that the entire production and distribution plan can be optimized independently in each time period. It is shown that the proposed decomposition methods yield significant computational savings, and temporal decomposition is shown to be the superior deco...

119 citations

Journal ArticleDOI
TL;DR: An outer-approximation algorithm to obtain the global optimum of a nonconvex mixed-integer nonlinear programming (MINLP) model that is used to represent the scheduling of crude oil movement at the front-end of a petroleum refinery.

119 citations

Journal ArticleDOI
TL;DR: The highly nonlinear planetary-entry optimal control problem is formulated as a sequence of convex problems to facilitate rapid solution to avoid nonconvex control constraint.
Abstract: In this paper, the highly nonlinear planetary-entry optimal control problem is formulated as a sequence of convex problems to facilitate rapid solution. The nonconvex control constraint is avoided ...

119 citations

Journal ArticleDOI
TL;DR: The coordination complexity of approximate price-directive decomposition PDD for the general block-angular convex resource sharing problem in K blocks and M nonnegative block-separable coupling constraints is studied and the fastest currently-known deterministic approximation algorithm for minimum-cost multicommodity flows is obtained.
Abstract: The general block-angular convex resource sharing problem in K blocks and M nonnegative block-separable coupling constraints is considered. Applications of this model are in combinatorial optimization, network flows, scheduling, communication networks, engineering design, and finance. This paper studies the coordination complexity of approximate price-directive decomposition PDD for this problem, i.e., the number of iterations required to solve the problem to a fixed relative accuracy as a function of K and M. First a simple PDD method based on the classical logarithmic potential is shown to be optimal up to a logarithmic factor in M in the class of all PDD methods that work with the original unrestricted blocks. It is then shown that logarithmic and exponential potentials generate a polylogarithmically-optimal algorithm for a wider class of PDD methods which can restrict the blocks by the coupling constraints. As an application, the fastest currently-known deterministic approximation algorithm for minimum-cost multicommodity flows is obtained.

119 citations

Journal ArticleDOI
TL;DR: In this paper, the problem of minimizing the operating cost of a power system by proper selection of the active and reactive productions is formulated as a nonlinear programming problem, and an efficient computational procedure based on the Newton-Raphson method for solving the power-flow equations and on the dual Lagrangian variables of the Kuhn and Tucker theorem is discussed.
Abstract: The general problem of minimizing the operating cost of a power system by proper selection of the active and reactive productions is formulated as a nonlinear programming problem in accordance with previous work by Carpentier of Electricitede France. This general problem is particularized to the minimization of transmission line losses by suitable selection of the reactive productions and transformer tap settings. An efficient computational procedure based on the Newton-Raphson method for solving the power-flow equations and on the dual (Lagrangian) variables of the Kuhn and Tucker theorem is discussed. This minimization procedure has been applied successfully to a 500-node system studied by the Bonneville Power Administration for which an effective power-flow program had been developed previously. The dual variables associated with the primary (electrical) variables are obtained in the course of the computation, and their engineering significance for power system design and tariffication is emphasized. The procedure has been extended to the general case of combined active and reactive optimization.

119 citations


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