Abstact: A method is presented for direct trajectory optimization and costate estimation using global collocation at Legendre-Gauss-Radau (LGR) points. The method is formulated first by casting the dynamics in integra...
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Mission engineers have detected an unexpected anomaly on six spacecraft during lowaltitude gravity-assist maneuvers around Earth. This Earth flyby anomaly involves an acceleration that, to date, researchers cannot acc...
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This paper deals with the synthesis of optimal trajectories for aerobatic air races. A typical example of an air race event is the Red Bull Air Race World Series, where high-performance aerobatic aircraft fly a prescr...
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The multifan multistage station ventilation method has been widely popularized and applied in the underground mines of China since 1984. And the remarkable economic and social benefits have been obtained. The method h...
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ISBN:
(纸本)9787564603441
The multifan multistage station ventilation method has been widely popularized and applied in the underground mines of China since 1984. And the remarkable economic and social benefits have been obtained. The method has many advantages of having the high effective air volume efficiency and regulating and controlling easily air volume and economizing energy. But designing the optimum multifan multistage station ventilation network is a complex task. Sponsored by China National Nonferrous Industrial Company(CNNC), this task is satisfactorily solved by research and practice for nine years. The development in the field is reviewed. By converting the equation of the branch network to a problem of the equivalent nonlinear programming, this paper proves that the total sum of the energy loss in every branch will be minmum when the airflow distribution network system is in a balanced state. It also points out the energy meaning for the node method to solve the network equations and gives the unique existence theorem of the solution of a conclusions by using an example. network balance equation. And it explains these
The design of sheet pile walls by lower bound limit analysis is considered. The design problem involves the determination of the necessary yield moment of the wall, the wall depth and the anchor force such that the st...
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The design of sheet pile walls by lower bound limit analysis is considered. The design problem involves the determination of the necessary yield moment of the wall, the wall depth and the anchor force such that the structure is able to sustain the given loads. This problem is formulated as a nonlinear programming problem where the yield moment of the wall is minimized subject to equilibrium and yield conditions. The finite element discretization used enables exact fulfillment of these conditions and thus, according to the lower bound theorem, the solutions are safe. (C) 2004 Elsevier Ltd. All rights reserved.
This paper describes and analyzes an algorithmic framework for solving nonlinear programming problems in which strict complementarity conditions and constraint qualifications are not necessarily satisfied at a solutio...
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This paper describes and analyzes an algorithmic framework for solving nonlinear programming problems in which strict complementarity conditions and constraint qualifications are not necessarily satisfied at a solution. The framework is constructed from three main algorithmic ingredients. The first is any conventional method for nonlinear programming that produces estimates of the Lagrange multipliers at each iteration;the second is a technique for estimating the set of active constraint indices;the third is a stabilized Lagrange - Newton algorithm with rapid local convergence properties. Results concerning rapid local convergence and global convergence of the proposed framework are proved. The approach improves on existing approaches in that less restrictive assumptions are needed for convergence and/or the computational workload at each iteration is lower.
The complexity of many decision problems may require the formulation of nonlinear models able to consider in a more realistic way its physical, chemical, economical, and biological properties. With modern sophisticati...
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ISBN:
(纸本)0889865264
The complexity of many decision problems may require the formulation of nonlinear models able to consider in a more realistic way its physical, chemical, economical, and biological properties. With modern sophistication of data measurements and structures, and computing capabilities, the models can represent real problems with less aggregation levels, improving their dimensions by larger number of variables and parameters submitted to more constraints to exhibit feasible solutions to practical problems. Models with dynamic structure as: (i) marine multi-species fishery management, and (ii) optimal electric energy short-term generation scheduling for complex hydro-thermal systems can be constructed. Coupled sets of discrete-time difference equations describe the interacting dynamics of natural resources and the environment, and optimal control theory can be applied to build model structure and to parameters estimation, but the increase in model complexities as nonlinearities, time delays, supplementary inequality constraints on the state and the control variables imply critical numerical difficulties. Reliable nonlinear programming numerical optimization methods can deal with these questions efficiently.
In this paper, a new method is presented to deal with nonconvex nonlinear inequality constrained problem by using the idea of epsilon-effective set. It is only required to solve two systems of linear equations per sin...
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In this paper, a new method is presented to deal with nonconvex nonlinear inequality constrained problem by using the idea of epsilon-effective set. It is only required to solve two systems of linear equations per single iteration. The theoretical analysis shows that the algorithm is global convergence under some suitable conditions. (c) 2004 Elsevier Inc. All rights reserved.
An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstr...
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An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem. Furthermore, under some assumptions, the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem. Therefore, f^om the theoretical point of view, a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well-known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented.
We investigate the possibility of solving mathematical programs with complementarity constraints (MPCCs) using algorithms and procedures of smooth nonlinear programming. Although MPCCs do not satisfy a constraint qual...
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We investigate the possibility of solving mathematical programs with complementarity constraints (MPCCs) using algorithms and procedures of smooth nonlinear programming. Although MPCCs do not satisfy a constraint qualification, we establish sufficient conditions for their Lagrange multiplier set to be nonempty. MPCCs that have nonempty Lagrange multiplier sets and satisfy the quadratic growth condition can be approached by the elastic mode with a bounded penalty parameter. In this context, the elastic mode transforms MPCC into a nonlinear program with additional variables that has an isolated stationary point and local minimum at the solution of the original problem, which in turn makes it approachable by sequential quadratic programming (SQP) algorithms. One such algorithm is shown to achieve local linear convergence once the problem is relaxed. Under stronger conditions, we also prove superlinear convergence to the solution of an MPCC using an adaptive elastic mode approach for an SQP algorithm recently analyzed in an MPCC context in [R. Fletcher, S. Leyffer, S. Sholtes, and D. Ralph, Local Convergence of SQP Methods for Mathematical Programs with Equilibrium Constraints, Tech. report NA 210, University of Dundee, Dundee, UK, 2002]. Our assumptions are more general since we do not use a critical assumption from that reference. In addition, we show that the elastic parameter update rule will not interfere locally with the superlinear convergence once the penalty parameter is appropriately chosen.
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