In this paper, we consider a nonlinear programming problem for which the constraint set may be infeasible. We propose an algorithm based on a large family of augmented Lagrangian functions and analyze its global conve...
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In this paper, we consider a nonlinear programming problem for which the constraint set may be infeasible. We propose an algorithm based on a large family of augmented Lagrangian functions and analyze its global convergence properties taking into account the possible infeasibility of the problem. We show that, in a finite number of iterations, the algorithm stops detecting the infeasibility of the problem or finds an approximate feasible/optimal solution with any required precision. We illustrate, by means of numerical experiments, that our algorithm is reliable for different Lagrangian/penalty functions proposed in the literature.
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.
Emissions from passenger ferries operating in urban harbors may contribute significantly to emissions inventories and commuter exposure to air pollution. In particular, ferries are problematic because of high emission...
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Emissions from passenger ferries operating in urban harbors may contribute significantly to emissions inventories and commuter exposure to air pollution. In particular, ferries are problematic because of high emissions of oxides of nitrogen (NO.) and particulate matter (PM) from primarily unregulated diesel engines. This paper explores technical solutions to reduce pollution from passenger ferries operating in the New York-New Jersey Harbor. The paper discusses and demonstrates a mixed-integer, non-linear programming model used to identify optimal control strategies for meeting NOx and PM reduction targets for 45 privately owned commuter ferries in the harbor. Results from the model can be used by policy-makers to craft programs aimed at achieving least-cost reduction targets.
We present a primal-dual interior-point algorithm with a filter line-search method for nonlinear programming. Local and global convergence properties of this method were analyzed in previous work. Here we provide a co...
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We present a primal-dual interior-point algorithm with a filter line-search method for nonlinear programming. Local and global convergence properties of this method were analyzed in previous work. Here we provide a comprehensive description of the algorithm, including the feasibility restoration phase for the filter method, second-order corrections, and inertia correction of the KKT matrix. Heuristics are also considered that allow faster performance. This method has been implemented in the IPOPT code, which we demonstrate in a detailed numerical study based on 954 problems from the CUTEr test set. An evaluation is made of several line-search options, and a comparison is provided with two state-of-the-art interior-point codes for nonlinear programming.
In this paper, we investigate the use of an exact primal-dual penalty approach within the framework of an interior-point method for nonconvex nonlinear programming. This approach provides regularization and relaxation...
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In this paper, we investigate the use of an exact primal-dual penalty approach within the framework of an interior-point method for nonconvex nonlinear programming. This approach provides regularization and relaxation, which can aid in solving ill-behaved problems and in warmstarting the algorithm. We present details of our implementation within the LOQO algorithm and provide extensive numerical results on the CUTEr test set and on warmstarting in the context of quadratic, nonlinear, mixed integer nonlinear, and goal programming.
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.
We propose a monotone descent active set QP-free method for inequality constrained optimization that ensures the feasibility of all iterates and allows for iterates on the boundary of the feasible set. The study is mo...
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We propose a monotone descent active set QP-free method for inequality constrained optimization that ensures the feasibility of all iterates and allows for iterates on the boundary of the feasible set. The study is motivated by the Facchinei - Fischer - Kanzow active set identification technique for nonlinear programming and variational inequalities [ F. Facchinei, A. Fischer, and C. Kanzow, SIAM J. Optim., 9 ( 1999), pp. 14 - 32]. Distinguishing features of the proposed method compared with existing QP-free methods include lower subproblem costs and a fast convergence rate under milder assumptions. Specifically, four reduced linear systems with a common coefficient matrix involving only constraints in a working set are solved at each iteration. To determine the working set, the method makes use of multipliers from the last iteration, eliminating the need to compute a new estimate, and no additional linear systems are solved to select linearly independent constraint gradients. A new technique is presented to avoid possible ill-conditioned Newton systems caused by dual degeneracy. It is shown that the method converges globally to KKT points under the linear independence constraint qualification (LICQ), and the asymptotic rate of convergence is Q-superlinear under an additional strong second-order sufficient condition (SSOSC) without strict complementarity.
In accord with the practical engineering design conditions, a nonlinear programming model is constructed for maximizing the fatigue life of V-belt drive in which some polymorphic uncertainties are incorporated. For a ...
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In accord with the practical engineering design conditions, a nonlinear programming model is constructed for maximizing the fatigue life of V-belt drive in which some polymorphic uncertainties are incorporated. For a given satisfaction level and a confidence level, an equivalent formulation of this uncertain optimization model is obtained where only interval parameters are involved. Based on the concepts of maximal and minimal range inequalities for describing interval inequality, the interval parameter model is decomposed into two standard nonlinear programming problems, and an algorithm, called two-step based sampling algorithm, is developed to find an interval optimal solution for the original problem. Case study is employed to demonstrate the validity and practicability of the constructed model and the algorithm.
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.
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