The paper considers an example of Wachter and Biegler which is shown to converge to a nonstationary point for the standard primal-dual interior-point method for nonlinear programming. The reason for this failure is an...
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The paper considers an example of Wachter and Biegler which is shown to converge to a nonstationary point for the standard primal-dual interior-point method for nonlinear programming. The reason for this failure is analyzed and a heuristic resolution is discussed. The paper then characterizes the performance of LOQO, a line-search interior-point code, on a large test set of nonlinear programming problems. Specific types of problems which can cause LOQO to fail are identified.
We propose a multidimensional filter SQP *** multidimensional filter technique proposed by Gould et al.[SIAM ***.,2005]is extended to solve constrained optimization *** our proposed algorithm,the constraints are parti...
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We propose a multidimensional filter SQP *** multidimensional filter technique proposed by Gould et al.[SIAM ***.,2005]is extended to solve constrained optimization *** our proposed algorithm,the constraints are partitioned into several parts,and the entry of our filter consists of these different *** only the criteria for accepting a trial step would be relaxed,but the individual behavior of each part of constraints is *** feature is that the undesirable link between the objective function and the constraint violation in the filter acceptance criteria *** other is that feasibility restoration phases are unnecessary because a consistent quadratic programming subproblem is *** prove that our algorithm is globally convergent to KKT points under the constant positive generators(CPG)condition which is weaker than the well-known Mangasarian-Fromovitz constraint qualification(MFCQ)and the constant positive linear dependence(CPLD).Numerical results are presented to show the efficiency of the algorithm.
A new inexact-restoration method for nonlinear programming is introduced. The iteration of the main algorithm has two phases. In Phase 1, feasibility is improved explicitly;in Phase 2, optimality is improved on a tang...
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A new inexact-restoration method for nonlinear programming is introduced. The iteration of the main algorithm has two phases. In Phase 1, feasibility is improved explicitly;in Phase 2, optimality is improved on a tangent approximation of the constraints. Trust regions are used for reducing the step when the trial point is not good enough. The trust region is not centered in the current point, as in many nonlinear programming algorithms, but in the intermediate more feasible point. Therefore, in this semifeasible approach, the more feasible intermediate point is considered to be essentially better than the current point. This is the first method in which intermediate-point-centered trust regions are combined with the decrease of the Lagrangian in the tangent approximation to the constraints. The merit function used in this paper is also new: it consists of a convex combination of the Lagrangian and the nonsquared norm of the constraints. The Euclidean norm is used for simplicity, but other norms for measuring infeasibility are admissible. Global convergence theorems are proved, a theoretically justified algorithm for the first phase is introduced, and some numerical insight is given.
In this paper, we propose a new nonmonotone algorithm using the sequential systems of linear equations, which is an infeasible QP-free method. We use neither a penalty function nor a filter. Therefore, it is unnecessa...
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In this paper, we propose a new nonmonotone algorithm using the sequential systems of linear equations, which is an infeasible QP-free method. We use neither a penalty function nor a filter. Therefore, it is unnecessary to choose a problematic penalty parameter. The new algorithm only needs to solve three systems of linear equations with the same nonsingular coefficient matrix. Under some suitable conditions, the global convergence is established. Some numerical results are also presented.
In this paper, we propose a novel objective penalty function for inequality constrained optimization problems. The objective penalty function differs from any existing penalty function and also has two desired feature...
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In this paper, we propose a novel objective penalty function for inequality constrained optimization problems. The objective penalty function differs from any existing penalty function and also has two desired features: exactness and smoothness if the constraints and objective function are differentiable. All exact penalty result is proved for the objective penalty function. In addition to these results, based on the objective penalty function, we develop an algorithm for solving the original problem and show its convergence under some mild conditions. (C) 2004 Elsevier Ltd. All rights reserved.
This paper deals with a new variant of the inexact restoration method of Fischer and Friedlander (Comput Optim Appl 46:333-346, 2010) for nonlinear programming. We propose an algorithm that replaces the monotone line ...
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This paper deals with a new variant of the inexact restoration method of Fischer and Friedlander (Comput Optim Appl 46:333-346, 2010) for nonlinear programming. We propose an algorithm that replaces the monotone line search performed in the tangent phase by a non-monotone one, using the sharp Lagrangian as merit function. Convergence to feasible points satisfying the convex approximate gradient projection condition is proved under mild assumptions. Numerical results on representative test problems show that the proposed approach outperforms the monotone version when a suitable non-monotone parameter is chosen and is also competitive against other globalization strategies for inexact restoration.
One of typical problems in water resources system modeling is derivation of optimal operating policy for reservoir to ensure water is used more efficiently. This paper introduces optimization analysis to determine mon...
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One of typical problems in water resources system modeling is derivation of optimal operating policy for reservoir to ensure water is used more efficiently. This paper introduces optimization analysis to determine monthly reservoir operating policies for five scenarios of predetermined cropping patterns for Koga irrigation scheme, Ethiopia. The objective function of the model was set to minimize the sum of squared deviation (SSD) from the desired targeted supply. Reservoir operation under different water availability and thresholds of irrigation demands has been analyzed by running a chance constraint nonlinear programming model based on uncertain inflow data. The model was optimized using Microsoft Excel Solver. The lowest SSD and vulnerability, and the highest volumetric reliability were gained at irrigation deficit thresholds of 20% under scenario I, 30% under scenario II, III and V, and at 40% under scenario IV when compensation release is permitted for downstream environment. These thresholds of deficits could be reduced by 10 % for all scenarios if compensation release is not permitted. In conclusion the reservoir water is not sufficient enough to meet 100% irrigation demand for design command areas of 7,000 ha. The developed model could be used for real time reservoir operation decision making for similar reservoir irrigation systems. In this specific case study system, attempt should be made to evaluate the technical performance of the scheme and introduce a regulated deficit irrigation application.
To solving nonlinear control problems and especially nonlinear optimal control problems (NOCP), classical methods are not usually efficient. In this paper we introduce a new approach for solving this class of problems...
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To solving nonlinear control problems and especially nonlinear optimal control problems (NOCP), classical methods are not usually efficient. In this paper we introduce a new approach for solving this class of problems by using nonlinear programming Problem (NLPP). First, we transfer the original problem to a new problem in form of calculus of variations. Then we discretize the new problem and solve it by using NLPP packages. The solution of the NLPP is used to obtain the optimal control and states, which are the exact solution of the original problem (NOCP). What is more, a NLPP is transferred to a Linear programming Problem (LPP) which empower us to use powerful LP softwares. The degree of desirability is described for suboptimal approximate solutions. Also the nonlinear approximate solution and the optimal control are shown as a combination of polynomial functions or periodic functions. Finally, efficiency of our approach is confirmed by some numerical examples. (c) 2006 Published by Elsevier Inc.
This paper studies the ordinal and additive inconsistency problems of linguistic preference relations. First, the definition of ordinal consistency of a linguistic preference relation is proposed. Based on the definit...
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This paper studies the ordinal and additive inconsistency problems of linguistic preference relations. First, the definition of ordinal consistency of a linguistic preference relation is proposed. Based on the definition of adjacency matrix of a linguistic preference relation, the necessary and sufficient conditions of a linguistic preference relation being ordinally consistent are given. Then, a distance-based nonlinear programming method is developed to identify and adjust the ordinal and additive inconsistencies for linguistic preference relations. The proposed methods can not only solve the ordinal inconsistency, additive inconsistency problems, respectively, but also solve the ordinal and additive inconsistency problems simultaneously. Finally, numerical examples and comparative analysis are provided to show the effectiveness and advantages of the proposed methods.
The volume of data is increasing rapidly, which poses a great challenge for resource-constrained users to process and analyze. A promising approach for solving computation-intensive tasks over big data is to outsource...
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The volume of data is increasing rapidly, which poses a great challenge for resource-constrained users to process and analyze. A promising approach for solving computation-intensive tasks over big data is to outsource them to the cloud to take advantage of the cloud's powerful computing capability. However, it also brings privacy and security issues since the data uploaded to the cloud may contain sensitive and private information which should be protected. In this article, we address this problem and focus on the privacy-preserving and secure outsourcing of large-scale nonlinear programming problems (NLPs) subject to both linear constraints and nonlinear constraints. Large-scale NLPs play an important role in the field of data analytics but have not received enough attention in the context of cloud computing. In our outsourcing protocol, we first apply a secure and efficient transformation scheme at the client side to encrypt the private information of the considered NLP. Then, we use the reduced gradient method and generalized gradient method at the server side to solve the transformed large-scale NLPs under linear constraints and nonlinear constraints, respectively. We provide security analysis of the proposed protocol, and evaluate its performance via a series of experiments. The experimental results show that our protocol can efficiently solve large-scale NLPs and save much time for the client, providing a great potential for real applications.
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