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On the convergence of inexact augmented Lagrangian methods for problems with convex constraints

OPERATIONS RESEARCH LETTERS 2019年第3期47卷 185-189页

作者： Galvan, Giulio Lapucci, Matteo Univ Firenze DINFO Via Santa Marta 3 I-50139 Florence Italy

We consider the augmented Lagrangian method (ALM) for constrained optimization problems in the presence of convex inequality and convex abstract constraints. We focus on the case where the Lagrangian sub-problems are solved up to approximate stationary points, with increasing accuracy. We analyze two different criteria of approximate stationarity for the sub-problems and we prove the global convergence to stationary points of ALM in both cases. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Augmented Lagrangian method nonlinear programming Global convergence Convex constraints

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Development of an adaptation model by applying non-linear programming to compute adaptation deficiency in climatic hotspots

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PROGRESS IN DISASTER SCIENCE 2021年 12卷

作者： Akter, Marin Haque, Anisul Karim, Dewan Sadia Rahman, Munsur Salehin, Mashfiqus Kabir, Rubaiya Alim, Mohammad Abdul ul Haq, Mohammad Asif Bangladesh Univ Engn & Technol Dept Math Dhaka 1215 Bangladesh City Univ Dhaka 1215 Bangladesh Bangladesh Univ Engn & Technol Inst Water & Flood Management Dhaka 1000 Bangladesh Univ New South Wales Sch Phys Environm & Math Sci PEMS Canbera Australia Green Univ Bangladesh Elect & Elect Engn Dhaka Bangladesh Inst Water & Flood Management Dhaka 1000 Bangladesh

For the policy makers, risk-based planning to minimize future climatic risk needs decision on investment priority. This is particularly important where there are resource constraints, and in cases where the decisions depend on sociopolitical reality of the region. For the policy makers, it is also extremely important to know how a system will behave if investment is made on any specific adaptation in any specific location to minimize climatic risk in the region. To answer these questions, an Adaptation Model is developed in this study to compute adaptation deficiency for a location that will minimize climatic risk in that location. In this methodology, a system approach is followed by applying non-linear programming. The non-linear programming system is formulated by defining future climatic risk as the objective function where the risk is a non-linear function of hazard, exposure, vulnerability, where vulnerability is a linear combination of sensitivity and adaptive capacity. The system is restricted by seven constraints composed of different combinations of hazard, exposure, sensitivity and adaptive capacity. The model can be applied in any part of the world, for any climatic hazard, and for any time domain. In this study, the model is applied in Bangladesh coastal zone to compute adaptation deficiency required to be filled to minimize mid-century storm surge risk in the identified hotspots. The results show that out of 20 identified storm surge risk hotspots in Bangladesh coastal zone, cyclone shelter has the maximum adaptation deficiency in 10 hotspots followed by plantation in 8 hotspots. The output from the model can be used by the policy makers to decide on the most appropriate investment options for risk-based planning that will minimize future risks in the identified hotspots. The model shows the risk limit below which risk cannot be reduced. Any investment attempt on adaptation to reduce the risk beyond this limit will disrupt the system equilibrium and wi

关键词： Risk hotspot nonlinear programming System approach Risk minimization Adaptation deficiency Risk-based planning

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3D irregular packing in an optimized cuboid container

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IFAC-PapersOnLine 2019年第13期52卷 2014-2019页

作者： Litvinchev, I. Pankratov, A. Romanova, T. Faculty of Mechanical and Electrical Engineering San Nicolas de los Garza Mexico Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine Department of Mathematical Modelling and Optimal Design Kharkiv Ukraine

A packing problem for irregular 3D objects approximated by polyhedra is presented. The objects have to be packed into a cuboid of minimum height under continuous rotations, translations and minimum allowable distances between objects. The problem has various applications and arises, e.g. in additive manufacturing. Containment, distance and non-overlapping constraints are described using the phi-function technique. The irregular packing problem is formulated in the form of nonlinear programming problem. A solution algorithm is proposed based on a fast starting point algorithm and efficient local optimization procedure. © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： 3D printers Mathematical models nonlinear programming 3 D printing Continuous rotation Local optimizations Non linear optimization nonlinear programming problem Operation research Overlapping constraints Solution algorithms

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A Novel Collaborate Neural Dynamic System Model for Solving a Class of Min-Max Optimization Problems with an Application in Portfolio Management

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COMPUTER JOURNAL 2019年第7期62卷 1061-1085页

作者： Nazemi, Alireza Mortezaee, Marziyeh Shahrood Univ Technol Fac Math Sci POB ***-316 Shahrood Iran

In this paper, we describe a new neural network model for solving a class of non-smooth optimization problems with min-max objective function. The basic idea is to replace the min-max function by a smooth one using an entropy function. With this smoothing technique, the non-smooth problem is converted into an equivalent differentiable convex programming problem. A neural network model is then constructed based on Karush-Kuhn-Tucker optimality conditions. It is investigated that the proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem. As an application in economics, we use the proposed scheme to a min-max portfolio optimization problems. The effectiveness of the method is demonstrated by several numerical simulations.

关键词： non-smooth optimization neural network dynamic model convex programming entropy function nonlinear programming convergent stability

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Optimal day-ahead operation of user-level integrated energy system considering dynamic behaviour of heat loads and customers' heat satisfaction

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IET SMART GRID 2019年第3期2卷 320-326页

作者： Lv, Jiawei Zhang, Shenxi Cheng, Haozhong Fang, Sidun Shanghai Jiao Tong Univ Minist Educ Key Lab Control Power Transmiss & Convers 800 Dongchuan Rd Shanghai 200240 Peoples R China Nanyang Technol Univ Sch Elect & Elect Engn 50 Nanyang Ave Singapore 639798 Singapore

This study proposes a novel optimal day-ahead operation method for the user-level integrated energy system (IES), which can take into account the dynamic behaviour of heat loads and customers' heat satisfaction. First, based on the energy hub, the dynamic model of heat loads is added into IES. Additionally, the customers' heat satisfaction model is constructed by the variance of water temperature and punishment coefficient. Then, the optimal day-ahead operation model aimed at minimising the total cost is proposed. Constraints of energy purchase, operation of energy converters, loads, temperature and the variation of temperature are all contained. Piecewise linearisation and a standard modelling method are utilised to simplify the initial non-convex and non-linear problem to a quadratic programming problem. Finally, case studies are carried out on a practical calculation example. Results indicate that the total cost can be reduced by 5.6% when considering the dynamic behaviour of heat loads. Also, customers' heat satisfaction exerts a remarkable influence on the total cost.

关键词： power generation scheduling quadratic programming power distribution economics power generation economics nonlinear programming optimisation power markets user-level integrated energy system dynamic behaviour heat loads customers novel optimal day-ahead operation method energy hub dynamic model optimal day-ahead operation model total cost energy purchase energy converters standard modelling method

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A recourse-based nonlinear programming model for stream water quality management

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STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT 2012年第2期26卷 207-223页

作者： Li, Y. P. Huang, G. H. N China Elect Power Univ MOE Key Lab Reg Energy Syst Optimizat SC Energy & Environm Res Acad Beijing 102206 Peoples R China

A recourse-based nonlinear programming (RBNP) method is developed for stream water quality management under uncertainty. It can not only reflect uncertainties expressed as interval values and probability distributions but also address nonlinearity in the objective function. A 0-1 piecewise linearization approach and an interactive algorithm are advanced for solving the RBNP model. The RBNP is applied to a case of planning stream water quality management. The RBNP modeling system can provide an effective linkage between environmental regulations and economic implications expressed as penalties or opportunity losses caused by improper policies. The solutions can be used for generating a variety of alternatives under different combinations of pre-regulated targets, which are also associated with different water-quality-violation risk levels and varied potential economic penalty or loss values.

关键词： nonlinear programming 0-1 piecewise Planning Stochastic with recourse Water quality Uncertainty

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Learning to steer nonlinear interior-point methods

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EURO JOURNAL ON COMPUTATIONAL OPTIMIZATION 2019年第4期7卷 381-419页

作者： Kuhlmann, Renke Ctr Ind Math ZeTeM Optimizat & Optimal Control Bibliothekstr 5 D-28359 Bremen Germany

Interior-point or barrier methods handle nonlinear programs by sequentially solving barrier subprograms with a decreasing sequence of barrier parameters. The specific barrier update rule strongly influences the theoretical convergence properties as well as the practical efficiency. While many global and local convergence analyses consider a monotone update that decreases the barrier parameter for every approximately solved subprogram, computational studies show a superior performance of more adaptive strategies. In this paper we interpret the adaptive barrier update as a reinforcement learning task. A deep Q-learning agent is trained by both imitation and random action selection. Numerical results based on an implementation within the nonlinear programming solver WORHP show that the agent successfully learns to steer the barrier parameter and additionally improves WORHP's performance on the CUTEst test set.

关键词： nonlinear programming Constrained optimization Interior-point algorithm Reinforcement learning Deep Q-learning

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Global energy and geopolitical risk: behavior of oil markets

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INTERNATIONAL JOURNAL OF ENERGY SECTOR MANAGEMENT 2019年第2期14卷 358-371页

作者： Alqahtani, Abdullah Taillard, Michael Suffolk Univ Boston MA 02114 USA Cent Michigan Univ Mt Pleasant MI 48859 USA

Purpose The question being assessed is whether changes in the degree of global geopolitical risk (GPR), as defined by the framework developed by Iacoviello (2018), can be used to improve allocative efficiency, thereby increasing investment returns on oil commodities. Design/methodology/approach Using the linear and nonlinear model, this paper analyzes the impact of GPR on returns of oil prices (BRENT, WTI and Organization of Petroleum Exporting Countries), as well as the short- and long-run relationship between GPR and oil prices. Findings The results of the impulse response function indicates that oil prices do not respond to shocks in GPR. The results of the Granger causality test show that oil returns are not caused by GPR. The regression analysis and autoregressive distributed lag results show that there is no significant impact of GPR on the returns of oil. Originality/value This is unique among the literature in that it identifies and isolates the relationship between GPR and oil market pricing. Insight into the lag in market response and the degree to which GPR can be used to estimate oil prices using curvilinear models are derived from the analysis.

关键词： Policy Correlation analysis Crude oil Econometric nonlinear programming Autoregressive

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A randomized nonmonotone adaptive trust region method based on the simulated annealing strategy for unconstrained optimization

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International Journal of Intelligent Computing and Cybernetics 2019年第3期12卷 389-399页

作者： Saman Babaie-Kafaki Saeed Rezaee Department of Mathematics Semnan UniversitySemnanIran

Purpose–The purpose of this paper is to employ stochastic techniques to increase efficiency of the classical algorithms for solving nonlinear optimization ***/methodology/approach–The well-known simulated annealing strategy is employed to search successive neighborhoods of the classical trust region(TR)***–An adaptive formula for computing the TR radius is suggested based on an eigenvalue analysis conducted on the memoryless Broyden-Fletcher-Goldfarb-Shanno updating ***,a(heuristic)randomized adaptive TR algorithm is developed for solving unconstrained optimization *** of computational experiments on a set of CUTEr test problems show that the proposed randomization scheme can enhance efficiency of the TR *** implications–The algorithm can be effectively used for solving the optimization problems which appear in engineering,economics,management,industry and other ***/value–The proposed randomization scheme improves computational costs of the classical TR ***,the suggested algorithm avoids resolving the TR subproblems for many times.

关键词： nonlinear programming Simulated annealing Adaptive radius Trust region method,Unconstrained optimization

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Managing the risk of supply chain bankruptcy in supply chain network redesign

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IFAC-PapersOnLine 2019年第13期52卷 2431-2436页

作者： Jahani, Hamed Alavifard, Farzad Ivanov, Dmitry Ghasemishabankareh, Behrooz School of Business IT and Logistics RMIT University Melbourne Australia Australian Centre of Quantitative Research Australia HWR Berlin Global Supply Chain and Operations Management Germany School of Science RMIT University Melbourne Australia

All vital operations of a supply chain network (SCN) are inherently affected by uncertainties and risks in the economic environment. In this study, we extend an existing SCN model by elaborating on stochastic price and demand, and integrating economic uncertainty. Financial performance and credit solvency are of utmost importance when analysing the financial status of an SCN. Each of these components focuses on a different aspect of investment attractiveness under various economic conditions, and in turn, facilitates access to capital for the companies involved. We extend the SCN model with financial performance optimisation approach to a novel model to include the trade-offs between two objective functions: (1) the total equity as the financial performance of the SC, and (2) the Altman's Z-score as the credit solvency factor of the company. The model ascertains the future profitability, leverage, and liquidity of the SC by determining the optimal levels of production and inventory in each facility of the new network design. We introduce a weighted sum method and a novel genetic algorithm (GA) solution approach to solve the resultant bi-objective mixed integer nonlinear programming problem. We illustrate the representation scheme required for the GA in this paper. © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Supply chains Economic and social effects Finance Genetic algorithms Integer programming nonlinear programming Risk management Stochastic models Stochastic systems Bankruptcy Insolvency Real Options Supply chain network design Supply chain risk management Z scores

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