A variant of the ellipsoid method for nonlinear programming is introduced to enhance the speed of convergence. This variant is based on a new simple scheme to reduce the ellipsoid volume by using two center cuts gener...
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A variant of the ellipsoid method for nonlinear programming is introduced to enhance the speed of convergence. This variant is based on a new simple scheme to reduce the ellipsoid volume by using two center cuts generated in two consecutive iterations of the ellipsoid method. Computational tests show a significant improvement in computational efficiency. The tests show that the improvement is more significant for larger-size problems.
The real alkaline cleaning wastewater (ACW) was treated by a process consisting of neutralization, NaClO oxidation and aluminum sulfate (AS) coagulation, and a novel response surface methodology coupled nonlinear prog...
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The real alkaline cleaning wastewater (ACW) was treated by a process consisting of neutralization, NaClO oxidation and aluminum sulfate (AS) coagulation, and a novel response surface methodology coupled nonlinear programming (RSM-NLP) approach was developed and used to optimize the oxidation coagulation process under constraints of relevant discharge standards. Sulfuric acid neutralization effectively removed chemical oxygen demand (COD), surfactant alkylphenol ethoxylates (OP-10) and silicate at the optimum pH of 7.0, with efficiencies of 62.3%, >82.7% and 94.2%, respectively. Coagulation and adsorption by colloidal hydrated silica formed during neutralization were the major removal mechanisms. NaClO oxidation achieved almost complete removal of COD, but was ineffective for the removal of surfactant OP-10. AS coagulation followed by oxidation can efficiently remove OP-10 with the formation of Si-O-Al compounds. The optimum conditions for COD <= 100 mg/L were obtained at hypo chlorite to COD molar ratio of 2.25, pH of 10.0 and AS dosage of 0.65 g Al/L, with minimum cost of 9.58 $/m(3) ACW. This study shows that the integrative RSM-NLP approach could effectively optimize the oxidation-coagulation process, and is attractive for techno-economic optimization of systems with multiple factors and threshold requirements for response variables. (C) 2017 Elsevier Ltd. All rights reserved.
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.
Leafy green vegetables are highly susceptible to microbial contamination because they are minimally processed. Pathogenic bacteria of concern include Escherichia coli O157:H7, Salmonella spp., and Listeria monocytogen...
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Leafy green vegetables are highly susceptible to microbial contamination because they are minimally processed. Pathogenic bacteria of concern include Escherichia coli O157:H7, Salmonella spp., and Listeria monocytogenes. Leafy greens are a highly perishable commodity, and in some cases have a postharvest shelf-life limited to one week. This study provides an approach to optimize storage temperature of leafy greens in the supply chain, considering the cost of refrigeration, sensory quality parameters (i.e., fresh appearance, wilting, browning, and off-odor), and microbial safety using nonlinear programming (NLP). The loss of sensory quality parameters was expressed as Arrhenius equations and pathogen growth were represented by three-phase linear (primary) and square-root (secondary) models. The objective function was refrigeration cost, which was to be minimized. The constraints were growth of pathogens and the loss of sensory characteristics. An interactive graphical user interface was developed in MATLAB. Pathogen growth is of more concern than loss of sensory quality in fresh-cut Iceberg lettuce when considering a shelf-life of up to two days, and the model indicates is difficult to maintain sensory qualities for longer shelf-life values. Browning is of maximum concern for fresh-cut Iceberg and Romaine lettuce, whereas off-odor is the biggest concern for fresh-cut chicory. (C) 2016 Elsevier Ltd. All rights reserved.
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.
Process yield, the percentage of processed product units passing inspection, is a standard numerical measure of process performance in the manufacturing industry. On the basis of the process yield expression, an index...
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Process yield, the percentage of processed product units passing inspection, is a standard numerical measure of process performance in the manufacturing industry. On the basis of the process yield expression, an index S-pk was developed to provide an exact measure of process yield for normally distributed processes. Most traditional studies measuring process capability are based on crisp estimates in which the output process measurements are precise. However, it is common that the measurements of process quality characteristics are insufficiently precise. Traditional approaches for evaluating process yield become unreliable in such cases. Therefore, this study formulates fuzzy numbers to describe the quality characteristic measurements and applies two methods to construct the fuzzy estimation for S-pk. A nonlinear programming approach is provided to solve the a-level sets of the estimator, and a testing procedure is presented for making decisions. Finally, this concept is illustrated with an example and extended to solve the ranking problem of multiple yield indices. (c) 2013 Elsevier B.V. All rights reserved.
It is important to find a collision-free path for an unmanned underwater vehicle (UUV) and manipulator, from an initial to a goal configuration, when considering automated vehicle activity in and around subsea structu...
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It is important to find a collision-free path for an unmanned underwater vehicle (UUV) and manipulator, from an initial to a goal configuration, when considering automated vehicle activity in and around subsea structures. The problem is particularly acute when the combined motion of a vehicle and manipulator is considered, due to large numbers of degrees of freedom (DOF) which produce a large search space, the need for an efficient search algorithm, the need for defining cost functions without local minima, and an efficient representation of object geometries to avoid collisions. Over the past 20 years, a great deal of interest and progress has developed in robot path planning. This paper concentrates on efficient searching and object representation, while removing local minima. A novel approach to subsea vehicle/manipulator path planning using a nonlinear programming approach is presented. The central idea is to represent the free space of the workspace as a set of inequality constraints of a nonlinear programming problem, using the vehicle configuration variables. The goal configuration is designed as the unique global minimum point of the objective function. The initial configuration is treated as the start point for the nonlinear search. Then the numerical algorithm developed for solving the nonlinear programming problem is applied to solve the robot motion planning problem. Every immediate point generated using the nonlinear optimisation search method guarantees that it is in the free space and, therefore, is collision free. Mathematical foundations for constructive solid geometry, Boolean operations and approximation techniques are developed and are used to represent the free space of the robot workspace as a set of inequalities. The advantages of this approach are that mature techniques developed in the past thirty years, in nonlinear programming theory for the direction of search which guarantees convergence, efficiency and numerical robustness, can be appli
This article presents a nonlinear programming algorithm for finite element limit analysis (FELA) based on feasible arc searching technique (FAST). The proposed algorithm has the potential to significantly reduce the i...
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This article presents a nonlinear programming algorithm for finite element limit analysis (FELA) based on feasible arc searching technique (FAST). The proposed algorithm has the potential to significantly reduce the iteration numbers required for convergence, making it a valuable tool for solving complex optimization problems from FELA. The algorithm also introduces several new features to the existing methods, including: (i) a novel method for determining a reasonable updating step length;(ii) the avoidance of solving an additional "phase one problem" for finding an initial feasible point;and (iii) the proposition of an empirical criterion for detecting infeasibility problems. The effectiveness of the proposed approach has been demonstrated through several classic examples derived from geotechnical engineering. The initial two examples show the superior convergence speed of the novel approach compared to existing methods. Additionally, the third example highlights the efficacy of the feasibility detection criterion for problems involving both prescribed and unknown external forces.
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