This paper is concerned with the problem of investigating the properties and comparing the methods of nonlinear programming. The steepest-descent method, the method of Davidon, the method of conjugate gradients, and o...
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This paper is concerned with the problem of investigating the properties and comparing the methods of nonlinear programming. The steepest-descent method, the method of Davidon, the method of conjugate gradients, and other methods are investigated for the class of essentially nonlinear valley functions.
A parametric nonlinear programming problem in a metric space with an operator equality constraint in a Hilbert space is studied assuming that its lower semicontinuous value function at a chosen individual parameter va...
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A parametric nonlinear programming problem in a metric space with an operator equality constraint in a Hilbert space is studied assuming that its lower semicontinuous value function at a chosen individual parameter value has certain subdifferentiability properties in the sense of nonlinear (nonsmooth) analysis. Such subdifferentiability can be understood as the existence of a proximal subgradient or a Fr,chet subdifferential. In other words, an individual problem has a corresponding generalized Kuhn-Tucker vector. Under this assumption, a stable sequential Kuhn-Tucker theorem in nondifferential iterative form is proved and discussed in terms of minimizing sequences on the basis of the dual regularization method. This theorem provides necessary and sufficient conditions for the stable construction of a minimizing approximate solution in the sense of Warga in the considered problem, whose initial data can be approximately specified. A substantial difference of the proved theorem from its classical same-named analogue is that the former takes into account the possible instability of the problem in the case of perturbed initial data and, as a consequence, allows for the inherited instability of classical optimality conditions. This theorem can be treated as a regularized generalization of the classical Uzawa algorithm to nonlinear programming problems. Finally, the theorem is applied to the "simplest" nonlinear optimal control problem, namely, to a time-optimal control problem.
Up to now, batch distillation units have been controlled by means of dynamic programming or variational calculus, neither of which is easily implementable, particularly when multicomponent mixtures are considered. A q...
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Up to now, batch distillation units have been controlled by means of dynamic programming or variational calculus, neither of which is easily implementable, particularly when multicomponent mixtures are considered. A quite different approach based on an augmented Lagrangian nonlinear programming procedure is presented in this paper. For the maximum distillate problem, an optimal policy for linear time-dependent reflux is determined for each distillation period. From three examples involving binary and ternary mixtures, it appears that the Lagrangian procedure is an efficient tool for solving batch distillation problems.
A new programming algorithm for nonlinear constrained optimization problems is proposed. The method is based on the penalty function approach and thereby circumvents the necessity to maintain feasibility at each itera...
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A new programming algorithm for nonlinear constrained optimization problems is proposed. The method is based on the penalty function approach and thereby circumvents the necessity to maintain feasibility at each iteration, but it also behaves much like the gradient projection method. Although only first-order information is used, the algorithm converges asymptotically at a rate which is independent of the magnitude of the penalty term;hence, unlike the simple gradient method, the asymptotic rate of the proposed method is not affected by the ill-conditioning associated with the introduction of the penalty term. It is shown that the asymptotic rate of convergence of the proposed method is identical with that of the gradient projection method.
The paper extends prior work by the authors on LUQO, an interior point algorithm for nonconvex nonlinear programming. The specific topics covered include primal versus dual orderings and higher order methods, which at...
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The paper extends prior work by the authors on LUQO, an interior point algorithm for nonconvex nonlinear programming. The specific topics covered include primal versus dual orderings and higher order methods, which attempt to use each factorization of the Hessian matrix more than once to improve computational efficiency. Results show that unlike linear and convex quadratic programming, higher order corrections to the central trajectory are not useful for nonconvex nonlinear programming, but that a variant of Mehrotra's predictor-corrector algorithm can definitely improve performance.
Space shuttle trajectory design requires the optimization of highly-constrained, branched, atmospheric trajectories. This paper presents a general mathematical model for trajectory optimization incorporating multiple ...
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Space shuttle trajectory design requires the optimization of highly-constrained, branched, atmospheric trajectories. This paper presents a general mathematical model for trajectory optimization incorporating multiple simulation sections, state variable discontinuities, subarc elimination, branching, and six types of equality and inequality constraints. A solution is sought using a nonlinear programming approach based on SUMT, the sequential unconstrained minimization technique. Results of the numerical solution of a highly constrained space shuttle reentry problem are presented.
Presents a study on the NOP-2 modeling language for nonlinear programming. Definition of the modeling language for specifying general optimization problems; Effective solution for global optimization problems; Local o...
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Presents a study on the NOP-2 modeling language for nonlinear programming. Definition of the modeling language for specifying general optimization problems; Effective solution for global optimization problems; Local optimization programs which do not need analytical knowledge for a fast solving process.
We consider nonlinear programming problems the input data of which are not fixed, but vary in some real compact intervals. The aim of this paper is to determine bounds of the optimal values. We propose a general frame...
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We consider nonlinear programming problems the input data of which are not fixed, but vary in some real compact intervals. The aim of this paper is to determine bounds of the optimal values. We propose a general framework for solving such problems. Under some assumption, the exact lower and upper bounds are computable by using two non-interval optimization problems. While these two optimization problems are hard to solve in general, we show that for some particular subclasses they can be reduced to easy problems. Subclasses that are considered are convex quadratic programming and posynomial geometric programming.
This paper presents design and implementation of a single-phase three-wire (1phi3W) inverter with grid connection and active power filtering which is based on nonlinear programming and fast-zero-phase detection (FZPD)...
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This paper presents design and implementation of a single-phase three-wire (1phi3W) inverter with grid connection and active power filtering which is based on nonlinear programming and fast-zero-phase detection (FZPD) algorithm. The proposed inverter system can transmit photovoltaic power, compensate harmonic currents, supply reactive power, and balance power at source side even when the line voltages are highly distorted. Simulated and experimental results have verified the FZPD algorithm and demonstrated that when the voltage sources are highly distorted, the proposed inverter system can yield better power quality over that with conventional zero-crossing-detection algorithm.
A dual algorithm based on the smooth function proposed by Polyak (1988) is constructed for solving nonlinear programming problems with inequality constraints. It generates a sequence of points converging locally to a ...
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