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: In this paper, a characterization of algorithms that identify the optimal active constraints in a finite number of iterations is given, with a non-degeneracy assumption which is equivalent, in the standard nonlinear programming problem, to the assumption that there is a set of strictly complementary Lagrange multipliers.
Abstract: Nondegeneracy conditions that guarantee that the optimal active constraints are identified in a finite number of iterations are studied. Results of this type have only been established for a few algorithms, and then under restrictive hypothesis. The main result is a characterization of those algorithms that identify the optimal constraints in a finite number of iterations. This result is obtained with a nondegeneracy assumption which is equivalent, in the standard nonlinear programming problem, to the assumption that there is a set of strictly complementary Lagrange multipliers. As an important consequence of the authors’ results the way that this characterization applies to gradient projection and sequential quadratic programming algorithms is shown.
193 citations
TL;DR: It is shown that in structural flowsheet optimization problems that are formulated as mixed-integer nonlinear programming (MINLP) problems, modelling can have a great impact in the quality of solutions that are obtained, as well as on the computational efficiency.
192 citations
TL;DR: A modular and tractable framework for solving an adaptive distributionally robust linear optimization problem, where the worst-case expected cost is minimized over an ambiguity set of probability distributions, and it is shown that the adaptive Distributionally robustlinear optimization problem can be formulated as a classical robust optimization problem.
Abstract: We develop a modular and tractable framework for solving an adaptive distributionally robust linear optimization problem, where we minimize the worst-case expected cost over an ambiguity set of pro...
192 citations
TL;DR: The network proposed by M.P. Kennedy and L.O. Chua is justified from the viewpoint of optimization theory and the technique is extended to solve optimization problems, such as the least-squares problem.
Abstract: Neural networks for linear and quadratic programming are analyzed. The network proposed by M.P. Kennedy and L.O. Chua (IEEE Trans. Circuits Syst., vol.35, pp.554-562, May 1988) is justified from the viewpoint of optimization theory and the technique is extended to solve optimization problems, such as the least-squares problem. For quadratic programming, the network converges either to an equilibrium or to an exact solution, depending on whether the problem has constraints or not. The results also suggest an analytical approach to solve the linear system Bx=b without calculating the matrix inverse. The results are directly applicable to optimization problems with C/sup 2/ convex objective functions and linear constraints. The dynamics and applicability of the networks are demonstrated by simulation. The distance between the equilibria of the networks and the problem solutions can be controlled by the appropriate choice of a network parameter. >
191 citations
TL;DR: This paper reviews some of the most successful methods for unconstrained, constrained and nondifferentiable optimization calculations and suggests that practical considerations provide the main new ideas, and that subsequent theoretical studies give improvements to algorithms, coherence to the subject, and better understanding.
Abstract: This paper reviews some of the most successful methods for unconstrained, constrained and nondifferentiable optimization calculations. Particular attention is given to the contribution that theoretical analysis has made to the development of algorithms. It seems that practical considerations provide the main new ideas, and that subsequent theoretical studies give improvements to algorithms, coherence to the subject, and better understanding.
191 citations