In this paper, we use a generalized Fritz John condition to derive optimality conditions and duality results for a nonlinear programming with inequality constraints, under weak invexity with respect to different (eta(...
详细信息
In this paper, we use a generalized Fritz John condition to derive optimality conditions and duality results for a nonlinear programming with inequality constraints, under weak invexity with respect to different (eta(i))(i) assumption. The equivalence between saddle points and optima, and a characterization of optimal solutions are established under suitable generalized invexity requirements. Moreover, we prove weak, strong, converse and strict duality results for a Mond-Weir type dual. It is shown in this study, with examples, that the introduced generalized Fritz John condition combining with the invexity with respect to different (eta(i))(i) are especially easy in application and useful in the sense of sufficient optimality conditions and of characterization of solutions.
In 1988 Kennedy and Chua introduced the dynamical canonical nonlinear programming circuit (NPC) to solve in real time nonlinear programming problems where the objective function and the constraints are smooth (twice c...
详细信息
In 1988 Kennedy and Chua introduced the dynamical canonical nonlinear programming circuit (NPC) to solve in real time nonlinear programming problems where the objective function and the constraints are smooth (twice continuously differentiable) functions. In this paper, a generalized circuit is introduced (G-NPC), which is aimed at solving in real time a much wider class of nonsmooth nonlinear programming problems where the objective function and the constraints are assumed to satisfy only the weak condition of being regular functions. G-NPC, which derives from a natural extension of NPC, has a neural-like architecture and also features the presence of constraint neurons modeled by ideal diodes with infinite slope in the conducting region. By using the Clarke's generalized gradient of the involved functions, G-NPC is shown to obey a gradient system of differential inclusions, and its dynamical behavior and optimization capabilities, both for convex and nonconvex problems, are rigorously analyzed in the frame-' work of nonsmooth analysis and the theory of differential inclusions. In. the special important cas ' e of linear and quadratic programming problems, salient dynamical features of G-NPC, namely the presence of sliding modes, trajectory convergence infinite time, and the ability to compute the exact optimal solution of the problem being modeled, are uncovered and explained in the developed analytical framework.
A new method for linearly constrained nonlinear programming is proposed. This method follows affine scaling paths defined by systems of ordinary differential equations and it is fully parallelizable. The convergence o...
详细信息
A new method for linearly constrained nonlinear programming is proposed. This method follows affine scaling paths defined by systems of ordinary differential equations and it is fully parallelizable. The convergence of the method is proved for a nondegenerate problem with pseudoconvex objective function. In practice, the algorithm works also under more general assumptions on the objective function. Numerical results obtained with this computational method on several test problems are shown.
In this paper it is shown that, given a nonlinear programming problem with inequality constraints, it is possible to construct a continuously differentiable exact penalty function whose global or local unconstrained m...
详细信息
In this paper it is shown that, given a nonlinear programming problem with inequality constraints, it is possible to construct a continuously differentiable exact penalty function whose global or local unconstrained minimizers correspond to global or local solutions of the constrained problem.
To satisfy component concentration constraints in crude oil operations, it is necessary to blend different oil types, resulting in a mixed integer nonlinear programming (MINLP) formulation for the scheduling problem o...
详细信息
To satisfy component concentration constraints in crude oil operations, it is necessary to blend different oil types, resulting in a mixed integer nonlinear programming (MINLP) formulation for the scheduling problem of crude oil operations. Because of the intractability of such a nonlinear problem, approximate methods were proposed in the literature. However, by the existing methods, a composition concentration dicrepancy may occur, leading to an infeasible solution;or a feasible solution cannot be found even if such a solution exists for some cases. Based on a priority-slot modeling method, this paper copes with the crude-oil scheduling problem suffering from composition concentration discrepancy. To find a solution without composition concentration discrepancy, a valid inequality is added to the MINLP model. Also, the model size is significantly reduced by properly determining the number of slots. Then, a novel solution method is proposed. By this method, the problem is iteratively solved and, at each iteration step, only a reduced MILP problem is solved. Consequently, a solution can be found such that the composition concentration discrepancy is completely eliminated and it is computationally more efficient than the existing ones. Experiments are done to test the performance of the proposed method. Results show that the proposed method outperforms the existing ones.
In this work, we first study in detail the formulation of the primal-dual interior-point method for linear programming. We show that, contrary to popular belief, it cannot be viewed as a damped Newton method applied t...
详细信息
In this work, we first study in detail the formulation of the primal-dual interior-point method for linear programming. We show that, contrary to popular belief, it cannot be viewed as a damped Newton method applied to the Karush-Kuhn-Tucker conditions for the logarithmic barrier function problem. Next, we extend the formulation to general nonlinear programming, and then validate this extension by demonstrating that this algorithm can be implemented so that it is locally and Q-quadratically convergent under only the standard Newton method assumptions. We also establish a global convergence theory for this algorithm and include promising numerical experimentation.
A heat exchanger network design for a particular set of hot and cold stream duties requires multiple stream splits for minimum energy use. A modern NLP solver, FilterSQP, is applied to minimize a total cost function t...
详细信息
A heat exchanger network design for a particular set of hot and cold stream duties requires multiple stream splits for minimum energy use. A modern NLP solver, FilterSQP, is applied to minimize a total cost function that takes account of capital and energy costs. The best solution contains fewer exchangers than the initial network. There are multiple local optima at various cost levels. They contain different subsets of exchangers of the initial design, which constitutes a partial superstructure for the problem. Several optimization alternatives are examined: for the model formulation, leading to problems with different optimum costs, for the way the objective is written, which affects the formal degree of nonlinearity in the equations or objective, and for the way the solver operates. For each combination of options, tests were run using widely different initial values for the Trust Region size, a parameter in the solver. FilterSQP solved the network with impressive reliability and efficiency from several starting guesses, some of which were highly arbitrary. From even the most unpromising initial guesses, the solver converged to a local optimum in nearly all cases.
To analyze and resolve the contradiction of abnormal combustion and improving hydrogen-fueled engine power is the key for promoting the progress of hydrogen-fueled engine research. Optimal control is the most valuable...
详细信息
To analyze and resolve the contradiction of abnormal combustion and improving hydrogen-fueled engine power is the key for promoting the progress of hydrogen-fueled engine research. Optimal control is the most valuable technology for resolving this contradiction. In this paper, the optimal model of hydrogen-fueled engine for multi-variable, multi-objective, multi-constraint under the whole operating conditions was established. The technology was a combination of nonlinear programming theory and optimal calibration algorithm of genetic algorithm. Calibration process can be adjusted dynamically to match with the working conditions of engine by weighted function. It implements the unity of comprehensive performance optimization and individual optimization, and not only simplifies calibration process but also improves calibration speed. Furthermore, a new method that accurately and quickly calibrates MAP under the conditions of multi-variable, multi-goal and multi-constraint is provided to effectively resolve the contradiction of the abnormal combustion and improving hydrogen-fueled engine power. (C) 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.
This paper is devoted to the study of tilt stability in finite dimensional optimization via the approach of using the subgradient graphical derivative. We establish a new characterization of tilt-stable local minimize...
详细信息
This paper is devoted to the study of tilt stability in finite dimensional optimization via the approach of using the subgradient graphical derivative. We establish a new characterization of tilt-stable local minimizers for a broad class of unconstrained optimization problems in terms of a uniform positive-definiteness of the subgradient graphical derivative of the objective function around the point in question. By applying this result to nonlinear programming under the metric subregularity constraint qualification, we derive second-order characterizations and several new sufficient conditions for tilt stability. In particular, we show that each stationary point of a nonlinear programming problem satisfying the metric subregularity constraint qualification is a tilt-stable local minimizer if the classical strong second-order sufficient condition holds.
We prove that if a second order sufficient condition and a constraint regularity assumption hold, then for sufficiently small perturbations of the constraints and the objective function, the set of local minimizers re...
详细信息
We prove that if a second order sufficient condition and a constraint regularity assumption hold, then for sufficiently small perturbations of the constraints and the objective function, the set of local minimizers reduces to a singleton. Moreover, the minimizes and the associated multipliers are Lipschitzian functions of the parameter.
暂无评论