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COMPUTERS & CHEMICAL ENGINEERING 2022年 160卷 107707-107707页

作者： Zhang, Shulei Jia, Runda He, Dakuo Chu, Fei Mao, Zhizhong Northeastern Univ Sch Informat Sci & Engn Shenyang 110004 Peoples R China Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang 110004 Peoples R China Northeastern Univ Liaoning Key Lab Intelligent Diag & Safety Met In Shenyang 110004 Peoples R China China Univ Min & Technol Sch Informat & Control Engn Xuzhou 221116 Jiangsu Peoples R China

A general robust optimization framework is proposed to solve nonlinear programming under uncertainty. A compact convex data-driven uncertainty set is first conducted by leveraging the combined index statistic limit technique. It can effectively capture the correlations among uncertain variables by using the principal component analysis model, and eliminate the noise in massive uncertainty data. Based on the proposed uncertainty set, linearization is taken to approximate nonlinear optimization with inequality only constraints by using first-order Taylor approximation. By using the implicit function theorem, it is extended to a general formulation involving both inequality and equality constraints. Due to the potential limitation of first-order Taylor approximation, an iterative algorithm is designed to realize multiple linearization to search for a global robust solution under large perturbation. The efficiency of the proposed approach is verified on simulated numerical experiences, and the proposed method is applied to the industrial process of gold cyanidation leaching.(c) 2022 Elsevier Ltd. All rights reserved.

关键词： nonlinear programming Robust optimization Uncertainty set Statistic limit Principal component analysis

FORMULATING AND HEURISTIC SOLVING OF CONTACT PROBLEMS IN HYBRID DATA-DRIVEN COMPUTATIONAL MECHANICS

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arXiv 2023年

作者： Gebhardt, Cristian G. Lange, Senta Steinbach, Marc C. Allégaten 70 Bergen5007 Norway Leibniz Universität Hannover Institute of Applied Mathematics Welfengarten 1 Hannover30167 Germany

In this work we consider the hybrid Data-Driven Computational Mechanics (DDCM) approach, in which a smooth constitutive manifold is reconstructed to obtain a well-behaved nonlinear optimization problem (NLP) rather than the much harder discrete-continous NLP (DCNLP) of the direct DDCM approach. The key focus is on the addition of geometric inequality constraints to the hybrid DDCM formulation. Therein, the required constraint force leads to a contact problem in the form of a mathematical program with complementarity constraints (MPCC), a problem class that is still less complex than the DCNLP. For this MPCC we propose a heuristic quick-shot solution approach, which can produce verifiable solutions by solving up to four NLPs. We perform various numerical experiments on three different contact problems of increasing difficulty to demonstrate the potential and limitations of this *** Codes 74B20, 74M15, 90C30, 90C33, 90C59 © 2023, CC BY-NC-ND.

关键词： nonlinear programming

VARIATIONAL PROPERTIES OF DECOMPOSABLE FUNCTIONS. PART II: STRONG SECOND-ORDER THEORY

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arXiv 2023年

作者： Ouyang, Wenqing Milzarek, Andre The Chinese University of Hong Kong Shenzhen China

Local superlinear convergence of the semismooth Newton method usually requires the uniform invertibility of the generalized Jacobian matrix, e.g. BD-regularity or CD-regularity. For several types of nonlinear programming and composite-type optimization problems – for which the generalized Jacobian of the stationary equation can be calculated explicitly – this is characterized by the strong second-order sufficient condition. However, general characterizations are still not well understood. In this paper, we propose a strong second-order sufficient condition (SSOSC) for composite problems whose nonsmooth part has a generalized conic-quadratic second subderivative. We then discuss the relationship between the SSOSC and another second order-type condition that involves the generalized Jacobians of the normal map. In particular, these two conditions are equivalent under certain structural assumptions on the generalized Jacobian matrix of the proximity operator. Next, we verify these structural assumptions for C2-strictly decomposable functions via analyzing their second-order variational properties under additional geometric assumptions on the support set of the decomposition pair. Finally, we show that the SSOSC is further equivalent to the strong metric regularity condition of the subdifferential, the normal map, and the natural residual. Counterexamples illustrate the necessity of our assumptions. Copyright © 2023, The Authors. All rights reserved.

关键词： nonlinear programming

Equipment Development Scheme Decision Based on IFS-Choquet Integral Improved Matter Element Model

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Mathematical Problems in Engineering 2023年第1期2023卷

作者： Zhu, Nuojin Zhang, Huaiqiang Yang, Yang Shi, Boyuan Gao, Kun Department of Management Engineering and Equipment Economics Naval University of Engineering Wuhan430033 China

An optimized matter element decision method is proposed based on intuitionistic fuzzy set (IFS) and Choquet integral to solve the problems of equipment development scheme decision (e.g., the correlation of scheme attributes and the low decision reliability of evaluation results). First, the nonlinear programming problem of expert intuition fuzzy subjective and objective decision information difference is constructed using the Choquet integral method, and the measure values and related factors of decision attributes are solved using the optimization algorithm. Second, given the comprehensive contribution of attributes, the fuzzy measure Shapley value is employed to represent the attribute weight. Last, the matter element extension model is optimized using the attribute weight information and intuitionistic fuzzy score value, and a two-level evaluation strategy is formulated to determine the ranking and grade. On that basis, scientific decisions are made for several different schemes to be selected. © 2023 Nuojin Zhu et al.

关键词： nonlinear programming

A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networks

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arXiv 2023年

作者： Gratton, Serge Mercier, Valentin Riccietti, Elisa Toint, Philippe L. Université de Toulouse INP-ENSEEIHT IRIT Toulouse France Université de Toulouse ANITI CERFACS IRIT Toulouse France BRLi France Université de Lyon INRIA ENSL UCBL CNRS LIP UMR 5668 Lyon France University of Namur Namur Belgium

Multi-level methods are widely used for the solution of large-scale problems, because of their computational advantages and exploitation of the complementarity between the involved sub-problems. After a re-interpretation of multi-level methods from a block-coordinate point of view, we propose a multi-level algorithm for the solution of nonlinear optimization problems and analyze its evaluation complexity. We apply it to the solution of partial differential equations using physics-informed neural networks (PINNs) and consider two different types of neural architectures, a generic feedforward network and a frequency-aware network. We show that our approach is particularly effective if coupled with these specialized architectures and that this coupling results in better solutions and significant computational savings. Copyright © 2023, The Authors. All rights reserved.

关键词： nonlinear programming

Integration of solar field with multiple stage evaporator to sustain eco-energy in pulp and paper plant

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JOURNAL OF CLEANER PRODUCTION 2022年 333卷

作者： Pati, Smitarani Verma, Om Prakash Dr BR Ambedkar Natl Inst Technol Dept Instrumentat & Control Engn Jalandhar 144011 Punjab India

Deploying renewable energy to unit design energy-efficient technologies may fulfill the additional demand of various energy-intensive industries for their sustainability and resiliency. Multiple Stage Evaporator (MSE) is one of the most energy-intensive units used to extract the water content of the weak liquor in various industries, including the paper industry. This energy intensiveness may be reduced by integrating various Energy Reduction Schemes (ERSs). Hence, this work proposes a ERSs integrated MSE model to analyze its energy efficiency. These ERSs includes Thermo-Vapor Compressor, Steam-, Feed-Split, Feed Preheater, and Flash Tanks. Further, the performance of the proposed model is investigated under two important real-time plant complexities: Boiling Point Elevation and Fouling to achieve more realistic results. The performance analysis is initiated with the formulation of a nonlinear constrained optimization problem to increase the steam economy (SE). Also, the simulation is extended to validate at two different product concentrations (52% and 65%) by employing state-of art optimization algorithms: CONOPT, and SCA in GAMS and MATLAB respectively. The simulated results shows an increment 1.64% and 1.37% of SE for both 52% and 65% concentration of weak liquor respectively in case of CONOPT than SCA. Also, the waste heat of the condensate, feed, and product may be further utilized for the heat recovery by incorporating the flash tanks which leads to a countable energy saving. Eventually, integrating the solar fields: PTC and LFR ensures a notable reduction in conventional heat utilization by 85.96% and 92.85%, respectively and hence, enhance the energy efficiency.

关键词： Energy integration Multiple stage evaporator Performance optimization nonlinear programming Metaheuristic approach Plant complexities Solar renewable energy

Competitive facility location problem with foresight considering discrete-nature attractiveness for facilities: Model and solution

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COMPUTERS & OPERATIONS RESEARCH 2022年 146卷

作者： Latifi, Seyyed Ebrahim Tavakkoli-Moghaddam, Reza Fazeli, Esmaeel Arefkhani, Hessam Iran Univ Sci & Technol Dept Ind Engn Tehran Iran Univ Tehran Coll Engn Sch Ind Engn Tehran Iran Sharif Univ Technol Dept Civil Engn Tehran Iran

This paper addresses a bi-level mixed-integer nonlinear programming (MINLP) model for the competitive facility location problem in a closed-loop supply chain (CLSC), in which a firm (i.e., leader) aims at entering a market by locating new distribution and collection facilities, where a competitor (i.e., follower) already exists. The goal is to find the location and attractiveness of each facility going to be established by the leader who seeks to maximize its profit while also taking the follower's response into account. The attractiveness of each facility is a function of integer variables related to the facility's characteristics. Customer behavior is considered to be probabilistic based on the Huff gravity-based rule. To globally optimize the model, a procedure that handles the discrete decisions of the follower's problem is proposed. Afterward, by replacing the inner level convex program with its corresponding Karush-Kuhn-Tucker (KKT) conditions, the bi-level MINLP is converted into a single-level MINLP model, optimized by an improved branch-and-refine algorithm. Numerical experiments on randomly generated instances are conducted to illustrate the model's applicability. Moreover, through a computational analysis of the proposed model, the amount of gain the leader makes and the follower loses due to foresight in the competition are calculated

关键词： Competitive facility location nonlinear programming Leader-follower game Exact solution

Optimal Management of Ev Parking-Lot Charging/Discharging for Load Profile Peak Shaving and Valley Filling in Microgrids

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SSRN

SSRN 2023年

作者： Rezaei, Payman Akhbari, Mahdi Department of Electrical Engineering Shahed University Tehran Iran

The rapid and continuing growth in peak load power is one of the significant challenges facing electric utilities. Every year a considerable cost is imposed on governments to invest in the construction of new power plants or the development of existing power plants to provide peak demand, which will only be required for a short duration of the year. However, such massive investments may be eliminated by flattening the demand curve. By peak shaving and valley filling, operation costs will also be reduced, in addition to reducing or delaying investment costs. In this paper, the problem of flattening the demand curve is considered as a nonlinear optimization model. But with the increase in the penetration level of EVs in the grid and the increasing number of parameters and variables in a nonlinear model, it is necessary to spend either money or time. Therefore, the proposed model was first linearized by using the piecewise linear approximation technique. Furthermore, the uncertainty involved in the arrival and departure time of electric vehicles in the parking lot has been modeled using the two-point estimation method. Finally, a case study of a microgrid is done by implementing the developed model for ten-minute intervals in GAMS software using real-world data. The simulation results show the performance and accuracy of the proposed linear and non-deterministic models. A reduction of 25.3% in the peak value of the demand curve, along with a reduction of 80% in the time of the calculations, proves the effectiveness of the proposed model. © 2023, The Authors. All rights reserved.

关键词： nonlinear programming

DrNLA: Extending Verification to Non-linear Programs through Dual Re-writing

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arXiv 2023年

作者： Liu, Yuandong Cyrus Le, Ton-Chanh Antonopoulos, Timos Koskinen, Eric Nguyen, Thanhvu Stevens Institute of Technology United States Yale University United States George Mason University United States

For many decades, advances in static verification have focused on linear integer arithmetic (LIA) programs. Many real-world programs are, however, written with non-linear integer arithmetic (NLA) expressions, such as programs that model physical events, control systems, or nonlinear activation functions in neural networks. While there are some approaches to reasoning about such NLA programs, still many verification tools fall short when trying to analyze them. To expand the scope of existing tools, we introduce a new method of converting programs with NLA expressions into semantically equivalent LIA programs via a technique we call dual rewriting. Dual rewriting discovers a linear replacement for an NLA Boolean expression (e.g. as found in conditional branching), simultaneously exploring both the positive and negative side of the condition, and using a combination of static validation and dynamic generalization of counterexamples. While perhaps surprising at first, this is often possible because the truth value of a Boolean NLA expression can be characterized in terms of a Boolean combination of linearly-described regions/intervals where the expression is true and those where it is false. The upshot is that rewriting NLA expressions to LIA expressions beforehand enables off-the-shelf LIA tools to be applied to the wider class of NLA programs. We built a new tool DrNLA and show it can discover LIA replacements for a variety of NLA programs. We then applied our work to branching-time verification of NLA programs, creating the first set of such benchmarks (92 in total) and showing that DrNLA’s rewriting enable tools such as FuncTion and T2 to verify CTL properties of 42 programs that previously could not be verified. We also show a potential use of DrNLA assisting Frama-C in program slicing, and report that execution speed is not impacted much by rewriting. © 2023, CC BY.

关键词： nonlinear programming

A Fast Smoothing Newton Method for Bilevel Hyperparameter Optimization for SVC with Logistic Loss

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arXiv 2023年

作者： Wang, Yixin Li, Qingna School of Mathematics and Statistics Beijing Institute of Technology Beijing China Beijing Key Laboratory on MCAACI Key Laboratory of Mathematical Theory and Computation in Information Security Beijing Institute of Technology Beijing China

Support Vector Classification with logistic loss has excellent theoretical properties in classification problems where the label values are not continuous. In this paper, we reformulate the hyperparameter selection for SVC with logistic loss as a bilevel optimization problem in which the upper-level problem and the lower-level problem are both based on logistic loss. The resulting bilevel optimization model is converted to a single-level nonlinear programming (NLP) problem based on the KKT conditions of the lower-level problem. Such NLP contains a set of nonlinear equality constraints and a simple lower bound constraint. The second-order sufficient condition is characterized, which guarantees that the strict local optimizers are obtained. To solve such NLP, we apply the smoothing Newton method proposed in [32] to solve the KKT conditions, which contain one pair of complementarity constraints. We show that the smoothing Newton method has a superlinear convergence rate. Extensive numerical results verify the efficiency of the proposed approach and strict local minimizers can be achieved both numerically and theoretically. In particular, compared with other methods, our algorithm can achieve competitive results while consuming less time than other methods. Copyright © 2023, The Authors. All rights reserved.

关键词： nonlinear programming