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.
We propose a new constraint-handling approach for general constraints that is applicable to a widely used class of constrained derivative-free optimization methods. As in many methods that allow infeasible iterates, c...
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We propose a new constraint-handling approach for general constraints that is applicable to a widely used class of constrained derivative-free optimization methods. As in many methods that allow infeasible iterates, constraint violations are aggregated into a single constraint violation function. As in filter methods, a threshold, or barrier, is imposed on the constraint violation function, and any trial point whose constraint violation function value exceeds this threshold is discarded from consideration. In the new algorithm, unlike the filter method, the amount of constraint violation subject to the barrier is progressively decreased adaptively as the iteration evolves. We test this progressive barrier (PB) approach versus the extreme barrier (EB) with the generalized pattern search (Gps) and the lower triangular mesh adaptive direct search (LTMads) methods for nonlinear derivative-free optimization. Tests are also conducted using the Gps-filter, which uses a version of the Fletcher-Leyffer filter approach. We know that Gps cannot be shown to yield kkt points with this strategy or the filter, but we use the Clarke nonsmooth calculus to prove Clarke stationarity of the sequences of feasible and infeasible trial points for LTMads-PB. Numerical experiments are conducted on three academic test problems with up to 50 variables and on a chemical engineering problem. The new LTMads-PB method generally outperforms our LTMads-EB in the case where no feasible initial points are known, and it does as well when feasible points are known. which leads us to recommend LTMads-PB. Thus the LTMads- PB is a useful practical extension of our earlier LTMads-EB algorithm, particularly in the common case for real problems where no feasible point is known. The same conclusions hold for Gps-PB versus Gps-EB.
We consider first the differentiable nonlinear programming problem and study the asymptotic behavior of methods based on a family of penalty functions that approximate asymptotically the usual exact penalty function. ...
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We consider first the differentiable nonlinear programming problem and study the asymptotic behavior of methods based on a family of penalty functions that approximate asymptotically the usual exact penalty function. We associate two parameters to these functions: one is used to control the slope and the other controls the deviation from the exact penalty. We propose a method that does not change the slope for feasible iterates and show that for problems satisfying the Mangasarian-Fromovitz constraint qualification all iterates will remain feasible after a finite number of iterations. The same results are obtained for non-smooth convex problems under a Slater qualification condition.
In this paper,we improve the algorithm proposed by *** and *** in paper [1]. It is shown that the improved algorithm is possessed of global convergence and under some conditions it can obtain locally supperlinear conv...
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In this paper,we improve the algorithm proposed by *** and *** in paper [1]. It is shown that the improved algorithm is possessed of global convergence and under some conditions it can obtain locally supperlinear convergence which is not possessed by the original algorithm.
Arterial-branch intersections are important components of urban road network but are greatly ignored of its role in maintaining an efficient traffic operation in regional networks. Arterial-branch intersections are ge...
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Arterial-branch intersections are important components of urban road network but are greatly ignored of its role in maintaining an efficient traffic operation in regional networks. Arterial-branch intersections are generally featured with significant fluctuations in the flow ratio of the branch road to the arterial road. So, in order to adapt the signal timing to this kind of intersection, an optimization control algorithm based on fuzzy control and nonlinear programming (FCNP) was proposed. To verify this optimization algorithm, the Python and Vissim joint simulation was employed. Prior to the simulation, traffic flow data were collected in 12 consecutive hours at an arterial-branch intersection in China. The simulation results show that, after signal timing optimization with FCNP, the average vehicle queue length and delay reduced 25.8% and 17.3%, respectively, when compared with the performance of the traffic-actuated control, which also outperformed previous equivalent research. Besides, the overall operation of the intersection was verified to be greatly improved and stabilized by using the proposed algorithm. The findings of this study provide a reasonable solution of distributing the right-of-way at arterial-branch intersections and suggest the advantage of combining fuzzy control and nonlinear programming in dealing with the signal timing optimization.
Semi-penalty function methods, which are proposed by Nie, are new approaches combining sequential quadratic programming (SQP) methods and sequential penalty quadratical programming (SlQP) approaches. But in some cases...
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Semi-penalty function methods, which are proposed by Nie, are new approaches combining sequential quadratic programming (SQP) methods and sequential penalty quadratical programming (SlQP) approaches. But in some cases, the subproblem may be inconsistent in Nie's method. Therefore, we aim to overcome the inconsistence in this paper. We regard some constraints, which is satisfied in some point, as constraints. Other constraints are acted as penalty term. The convergent results are obtained. Further, we extend our new semi-penalty method to augmented Lagrangian penalty approaches. (C) 2003 Elsevier Inc. All rights reserved.
In this paper, a heap-based optimizer algorithm with chaotic search has been presented for the global solution of nonlinear programming problems. Heap-based optimizer (HBO) is a modern human social behavior-influenced...
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In this paper, a heap-based optimizer algorithm with chaotic search has been presented for the global solution of nonlinear programming problems. Heap-based optimizer (HBO) is a modern human social behavior-influenced algorithm that has been presented as an effective method to solve nonlinear programming problems. One of the difficulties that faces HBO is that it falls into locally optimal solutions and does not reach the global solution. To recompense the disadvantages of such modern algorithm, we integrate a heap-based optimizer with a chaotic search to reach the global optimization for nonlinear programming problems. The proposed algorithm displays the advantages of both modern techniques. The robustness of the proposed algorithm is inspected on a wide scale of different 42 problems including unimodal, multi-modal test problems, and CEC-C06 2019 benchmark problems. The comprehensive results have shown that the proposed algorithm effectively deals with nonlinear programming problems compared with 11 highly cited algorithms in addressing the tasks of optimization. As well as the rapid performance of the proposed algorithm in treating nonlinear programming problems has been proved as the proposed algorithm has taken less time to find the global solution.
This paper extends the concept of higher-order search directions within interior point methods to convex nonlinear programming. This includes the mathematical framework needed to compute the higher-order derivatives. ...
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This paper extends the concept of higher-order search directions within interior point methods to convex nonlinear programming. This includes the mathematical framework needed to compute the higher-order derivatives. The paper also highlights some special cases where the computation of these higher-order derivatives is simplified and a dimensional lifting procedure for transforming a large number of general nonlinear problems into one of these more efficient forms. The paper further describes the algorithmic development required to employ these higher-order search directions in a practical algorithm. Computational results are presented for a large number of test problems, highlighting higher-order methods' strong potential for decreasing iteration count and their case-by-case potential for decreasing CPU time.
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