Through the use of data reconciliation techniques, the level of process variable corruption due to measurement noise can be reduced and both process knowledge and control system performance can be improved. Process da...
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Through the use of data reconciliation techniques, the level of process variable corruption due to measurement noise can be reduced and both process knowledge and control system performance can be improved. Process data from systems governed by dynamic equations are typically reconciled using the Kalman filter or the extended Kalman filter. Unfortunately, chemical engineering systems often operate dynamically in highly nonlinear regions where the extended Kalman filter may be inaccurate. In addition, the Kalman filter may not be adequate in the presence of inequality constraints. Thus, a more robust means for reconciling process measurements for nonlinear dynamic systems is desirable. In this paper, a new method for nonlinear dynamic data reconciliation (NDDR) using nonlinear progamming is proposed. Through the use of enhanced simultaneous optimization and solution techniques the algorithm provides a general framework within which efficient state and parameter estimation can be performed. Extensions for the treatment of biased measurements are also discussed. We demonstrate the use of NDDR and its extensions on a reactor example.
The family of feasible methods for minimization with nonlinear constraints includes the nonlinear projected gradient method, the generalized reduced gradient method (GRG), and many variants of the sequential gradient ...
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The family of feasible methods for minimization with nonlinear constraints includes the nonlinear projected gradient method, the generalized reduced gradient method (GRG), and many variants of the sequential gradient restoration algorithm (SGRA). Generally speaking, a particular iteration of any of these methods proceeds in two phases. In the restoration phase, feasibility is restored by means of the resolution of an auxiliary nonlinear problem, generally a nonlinear system of equations. In the minimization phase, optimality is improved by means of the consideration of the objective function, or its Lagrangian, on the tangent subspace to the constraints. In this paper, minimal assumptions are stated on the restoration phase and the minimization phase that ensure that the resulting algorithm is globally convergent. The key point is the possibility of comparing two successive nonfeasible iterates by means of a suitable merit function that combines feasibility and optimality. The merit function allows one to work with a high degree of infeasibility at the first iterations of the algorithm. Global convergence is proved and a particular implementation of the model algorithm is described.
The real structured singular value (RSSV, or real mu) is a useful measure to analyze the robustness of linear systems subject to structured real parametric uncertainty, and surely a valuable design tool for the contro...
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The real structured singular value (RSSV, or real mu) is a useful measure to analyze the robustness of linear systems subject to structured real parametric uncertainty, and surely a valuable design tool for the control systems engineers. We formulate the RSSV problem as a nonlinear programming problem and use a new computation technique, F-modified subgradient (F-MSG) algorithm, for its lower bound computation. The F-MSG algorithm can handle a large class of nonconvex optimization problems and requires no differentiability. The RSSV computation is a well known NP hard problem. There are several approaches that propose lower and upper bounds for the RSSV. However, with the existing approaches, the gap between the lower and upper bounds is large for many problems so that the benefit arising from usage of RSSV is reduced significantly. Although the F-MSG algorithm aims to solve the nonconvex programming problems exactly, its performance depends on the quality of the standard solvers used for solving subproblems arising at each iteration of the algorithm. In the case it does not find the optimal solution of the problem, due to its high performance, it practically produces a very tight lower bound. Considering that the RSSV problem can be discontinuous, it is found to provide a good fit to the problem. We also provide examples for demonstrating the validity of our approach.
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.
An attempt is made to model a gas lift allocation problem as a nonlinear optimization form with a wide range of constraints covering deficiencies carried out by past studies. In this article, a rigorous nonlinear prog...
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An attempt is made to model a gas lift allocation problem as a nonlinear optimization form with a wide range of constraints covering deficiencies carried out by past studies. In this article, a rigorous nonlinear programming approach is used to maximize daily cash flow of a group of production wells under gas lift operation. First, an appropriate model is prepared for gas lift performance curve of each well by use of nonlinear logarithmic and polynomial regression. Afterward, a model is constructed and solved for daily cash flow under capacity and pressure constraints. Results show a significant increase in cash flow for an optimized case compared with the current gas allocation plan. Moreover, sensitivity analysis was performed for different variables showing that oil price and compressing cost must be considered in long-term gas lift allocation optimization.
This paper is aimed toward the definition of a new exact augmented Lagrangian function for two-sided inequality constrained problems. The distinguishing feature of this augmented Lagrangian function is that it employs...
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This paper is aimed toward the definition of a new exact augmented Lagrangian function for two-sided inequality constrained problems. The distinguishing feature of this augmented Lagrangian function is that it employs only one multiplier for each two-sided constraint. We prove that stationary points, local minimizers and global minimizers of the exact augmented Lagrangian function correspond exactly to KKT pairs, local solutions and global solutions of the constrained problem.
In this paper, we present a primal-dual interior-point method for solving nonlinear programming problems. It employs a Levenberg-Marquardt (LM) perturbation to the Karush-Kuhn-Tucker (KKT) matrix to handle indefinite ...
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In this paper, we present a primal-dual interior-point method for solving nonlinear programming problems. It employs a Levenberg-Marquardt (LM) perturbation to the Karush-Kuhn-Tucker (KKT) matrix to handle indefinite Hessians and a line search to obtain sufficient descent at each iteration. We show that the LM perturbation is equivalent to replacing the Newton step by a cubic regularization step with an appropriately chosen regularization parameter. This equivalence allows us to use the favorable theoretical results of Griewank (The modification of Newton's method for unconstrained optimization by bounding cubic terms, 1981), Nesterov and Polyak (Math. Program., Ser. A 108:177-205, 2006), Cartis et al. (Math. Program., Ser. A 127:245-295, 2011;Math. Program., Ser. A 130:295-319, 2011), but its application at every iteration of the algorithm, as proposed by these papers, is computationally expensive. We propose a hybrid method: use a Newton direction with a line search on iterations with positive definite Hessians and a cubic step, found using a sufficiently large LM perturbation to guarantee a steplength of 1, otherwise. Numerical results are provided on a large library of problems to illustrate the robustness and efficiency of the proposed approach on both unconstrained and constrained problems.
Due to their large variety of applications, complex optimization problems induced a great effort to develop efficient solution techniques, dealing with both continuous and discrete variables involved in nonlinear func...
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Due to their large variety of applications, complex optimization problems induced a great effort to develop efficient solution techniques, dealing with both continuous and discrete variables involved in nonlinear functions. But among the diversity of those optimization methods, the choice of the relevant technique for the treatment of a given problem keeps being a thorny issue. Within the process engineering context, batch plant design problems provide a good framework to test the performances of various optimization methods: on the one hand, two mathematical programming techniquesDICOPT++ and SBB, implemented in the GAMS environmentand on the other hand, one stochastic method, i.e., a genetic algorithm. Seven examples, showing an increasing complexity, were solved with these three techniques. The resulting comparison enables the evaluation of their efficiency in order to highlight the most appropriate method for a given problem instance. It was proved that the best performing method is SBB, even if the genetic algorithm (GA) also provides interesting solutions, in terms of quality as well as of computational time.
作者：
Kim, MinjaeMyongji Univ
Dept Mech Engn 116 Myongji Ro Yongin 17058 Gyeonggi Do South Korea
Conventional developed component matching methods for a series type hybrid electric vehicle have a high computational burden or component alternation researches have considered only a few parts without the weight vari...
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Conventional developed component matching methods for a series type hybrid electric vehicle have a high computational burden or component alternation researches have considered only a few parts without the weight variation of each component. To address such problems, this study presents a novel component matching method with nonlinear programming (NLP) for a series hybrid electric bus. The fuel consumption minimization problem is discretized in time and multistarting points are used with the variations of each component. The proposed matching method suggests to use novel initial standards for component matching such that both the computational efficiency and accuracy could be achieved simultaneously. As a result, the most fuel efficient component combination among 8 components could be found, where the results were verified with those of dynamic programming (DP).
In this paper, a new sequential quadratic programming (SQP) method of feasible directions is proposed and analyzed for nonlinear programming, where a feasible direction of descent can be derived from solving only one ...
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In this paper, a new sequential quadratic programming (SQP) method of feasible directions is proposed and analyzed for nonlinear programming, where a feasible direction of descent can be derived from solving only one QP subproblem. In particular, this method can produce automatically a revised direction with the explicit expression which can avoid Maratos effect without solving QP subproblem. The theoretical analysis shows that global and superlinear convergence can be induced. In the end, numerical experiment is given to illustrate the effectiveness of the method. (C) 2002 Elsevier Inc. All rights reserved.
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