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: A survey of algorithms and applications for the nonlinear knapsack problem, a nonlinear optimization problem with just one constraint, bounds on the variables, and a set of specially structured constraints such as generalized upper bounds (GUBs), is presented.
230 citations
TL;DR: A new derivative-free algorithm, ORBIT, is presented for unconstrained local optimization of computationally expensive functions, using a trust-region framework using interpolating Radial Basis Function models to interpolate nonlinear functions using fewer function evaluations than the polynomial models considered by present techniques.
Abstract: We present a new derivative-free algorithm, ORBIT, for unconstrained local optimization of computationally expensive functions. A trust-region framework using interpolating Radial Basis Function (RBF) models is employed. The RBF models considered often allow ORBIT to interpolate nonlinear functions using fewer function evaluations than the polynomial models considered by present techniques. Approximation guarantees are obtained by ensuring that a subset of the interpolation points is sufficiently poised for linear interpolation. The RBF property of conditional positive definiteness yields a natural method for adding additional points. We present numerical results on test problems to motivate the use of ORBIT when only a relatively small number of expensive function evaluations are available. Results on two very different application problems, calibration of a watershed model and optimization of a PDE-based bioremediation plan, are also encouraging and support ORBIT's effectiveness on blackbox functions for which no special mathematical structure is known or available.
230 citations
TL;DR: Three nonlinear optimization algorithms, namely, the Hooke and Jeeves' method, the quasi-Newton, and conjugate gradient search procedures are investigated for solving a radio communication system design problem that seeks an optimal location of a single transmitter, or that of multiple transmitters, in order to serve a specified distribution of receivers.
Abstract: This paper is concerned with the mathematical modeling and analysis of a radio communication system design problem that seeks an optimal location of a single transmitter, or that of multiple transmitters, in order to serve a specified distribution of receivers. The problem is modeled by discretizing the radio coverage region into a grid of receiver locations and by specifying a function that estimates the path-loss or signal attenuation for each receiver location, given a particular location for a transmitter that communicates with it. The resulting model is a nonlinear programming problem having an implicitly defined objective function of minimizing a measure of weighted path-losses. Specializations of three nonlinear optimization algorithms, namely, the Hooke and Jeeves' method, the quasi-Newton, and conjugate gradient search procedures are investigated for solving this problem. The technique described here is intended to interact with various propagation prediction models and may be used in a CAD system for radio communication system design.
229 citations
01 Jan 2009
TL;DR: A survey of the development of algorithms for enforcing nonnegativity constraints in scientific computation is given, with special emphasis on such constraints in least squares computations in numerical linear algebra and in nonlinear optimization.
Abstract: A survey of the development of algorithms for enforcing nonnegativity constraints in scientific computation is given. Special emphasis is placed on such constraints in least squares computations in numerical linear algebra and in nonlinear optimization. Techniques involving nonnegative low-rank matrix and tensor factorizations are also emphasized. Details are provided for some important classical and modern applications in science and engineering. For completeness, this report also includes an effort toward a literature survey of the various algorithms and applications of nonnegativity constraints in numerical analysis.
228 citations
TL;DR: In this paper, the authors address the optimization of supply chain design and planning under responsive criterion and economic criterion with the presence of demand uncertainty by using a probabilistic model for stock-out.
228 citations