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Rank-1 positive semidefinite matrix-based nonlinear programming formulation for AC OPF

INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS 2019年第10期29卷

作者： Ma, Minyue Fan, Lingling Univ S Florida Dept Elect Engn Tampa FL 33620 USA

Semidefinite programming (SDP) relaxation offers a tight relaxation to nonconvex alternating current optimal power flow (AC OPF) problems. When the solution obtained from SDP relaxation of AC OPF is a rank-1 positive semidefinite (PSD) matrix, this solution is exact to the original problem. Research efforts have been devoted to find a rank-1 PSD matrix. In this paper, a nonlinear programming formulation with the PSD matrix as the decision variable is proposed. The rank-1 PSD matrix constraint is equivalent to all 2x2 minors of the PSD matrix being zero. The main challenge of the proposed formulation is the large number of the quadratic equality constraints. For a system of N buses, there are CN2CN2 minor related constraints (For a 10-node system, this number is 2025). Graph decomposition-based approach is then implemented in this research to decompose a power grid into radial lines and three-node cycles. Enforcing the related submatrices PSD and rank-1 guarantees a full PSD rank-1 matrix. Case study results demonstrate that the proposed formulation can provide similar quality results with the original AC OPF formulation.

关键词： AC optimal power flow convex relaxation exactness conditions nonlinear programming

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Choosing the best facility layout using the combinatorial method of Gray relation analysis and nonlinear programming

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JOURNAL OF STATISTICS & MANAGEMENT SYSTEMS 2019年第6期22卷 1143-1161页

作者： Abdollahi, Parvin Aslam, Muhammad Yazdi, Ahmad Ahmadi Yazd Univ Dept Ind Engn Yazd Iran King Abdulaziz Univ Fac Sci Dept Stat Jeddah 21551 Saudi Arabia Isfahan Univ Technol Dept Ind & Syst Engn Esfahan *** Iran

Layout designing is one of the most useful research domains for improving the facility efficiency and human resources in organizations, since it composes the best layout designed by engineers to the organization by qualitative and quantitative criteria and choosing the best alternative. In this paper, a corrected non-linear programming method with Grey correlations has been used for choosing the best layout among the layouts produced by ALDEP software, because in choosing a layout design, several criteria with regard to the quality and quantity are simultaneously considered. The decision makers have to choose between Layout design alternatives and their choice have to consider all decision criteria. Wide range of approaches have been introduced to help decision makers this study presents an integrated model of Gray relation analysis and non-linear programming method and create some improvements on previous studies. By using the proposed method in this study, besides considering the variety of criteria, maximizing and minimizing the criteria has also been done simultaneously.

关键词： 97k80 Facility layout nonlinear programming Gray Relation Analysis (GRA)

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nonlinear programming Hybrid Beam-Column Element Formulation for Large-Displacement Elastic and Inelastic Analysis

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JOURNAL OF ENGINEERING MECHANICS 2018年第10期144卷

作者： Andriotis, C. P. Papakonstantinou, K. G. Koumousis, V. K. Penn State Univ Dept Civil & Environm Engn University Pk PA 16802 USA Natl Tech Univ Athens Dept Civil & Environm Engn Athens 15780 Greece

Modern structural analysis necessitates numerical formulations with advanced nonlinear attributes. To that end, numerous finite elements have been proposed, spanning from classical to hybrid standpoints. In addition to their individual features, all formulations originally stem from an underlying variational principle, which can be deemed as a unified energy metric of the system. The corresponding equations of structural equilibrium define a stationary point of the assumed principle. Following this logic in this work, the total potential energy is directly treated as an objective function, subject to some kinematic compatibility constraints, within the conceptions of nonlinear programming. The only approximated internal field is curvature, whereas displacements occur solely as nodal entities and Lagrange multipliers serve compatibility. Thereby, a new nonlinear programming hybrid element formulation is derived, which uses exact kinematic fields, can incorporate nonlinear assumptions of any extent, and is amenable to various applicable nonlinear programming algorithms. The suggested nonlinear program is presented in detail herein, together with its consistent second-order iterative solution procedure. The results obtained in benchmark nonlinear structural problems are validated and compared with OpenSees flexibility-based elements, showcasing notable performance in terms of accuracy, mesh density discretization, computational speed, and robustness.

关键词： nonlinear programming

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A unified convergence analysis of a second-order method of multipliers for nonlinear conic programming

arXiv

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arXiv 2021年

作者： Chen, Liang Zhu, Junyuan Zhao, Xinyuan School of Mathematics Hunan University Changsha410082 China School of Mathematics Beijing University of Technology Beijing100124 China

In this paper, we accomplish a unified convergence analysis of a second-order method of multipliers (i.e., a second-order augmented Lagrangian method) for solving the conventional nonlinear conic optimization problems. Specifically, the algorithm that we investigated incorporates a specially designed nonsmooth (generalized) Newton step to furnish a second-order update rule for the multipliers. We first show in a unified fashion that under a few abstract assumptions, the proposed method is locally convergent and possesses a (nonasymptotic) superlinear convergence rate, even though the penalty parameter is fixed and/or the strict complementarity fails. Subsequently, we demonstrate that, for the three typical scenarios, i.e., the classic nonlinear programming, the nonlinear second-order cone programming, and the nonlinear semidefinite programming, these abstract assumptions are nothing but exactly the implications of the iconic sufficient conditions that were assumed for establishing the Q-linear convergence rates of the method of multipliers without assuming the strict *** Codes Primary 65K05, 49J52, Secondary 90C22, 26E25 Copyright © 2021, The Authors. All rights reserved.

关键词： nonlinear programming

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nonlinear programming methods based on closed-form expressions for optimal train control

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2017年 82卷 102-123页

作者： Ye, Hongbo Liu, Ronghui Univ Leeds Inst Transport Studies Leeds LS2 9JT W Yorkshire England

This paper proposes a novel approach to solve the complex optimal train control problems that so far cannot be perfectly tackled by the existing methods, including the optimal control of a fleet of interacting trains, and the optimal train control involving scheduling. By dividing the track into subsections with constant speed limit and constant gradient, and assuming the train's running resistance to be a quadratic function of speed, two different methods are proposed to solve the problems of interest. The first method assumes an operation sequence of maximum traction-speedholding-coasting-maximum braking on each subsection of the track. To maintain the mathematical tractability, the maximum tractive and maximum braking functions are restricted to be decreasing and piecewisequadratic, based on which the terminal speed;travel distance and energy consumption of each operation can be calculated in a closed-form, given the initial speed and time duration of that operation. With these closed-form expressions, the optimal train control problem is formulated and solved as a nonlinear programming problem. To allow more flexible forms of maximum tractive and maximum braking forces, the second method applies a constant force on each subsection. Performance of these,two methods is compared through a case study of the classic single-train control on a single journey. The proposed methods are further utilised to formulate more complex optimal train control problems, including scheduling a subway line while taking train control into account, and simultaneously optimising the control of a leader-follower train pair under fixed-and moving-block signalling systems. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Optimal train control Energy consumption nonlinear programming Closed-form expression Subway line scheduling Simultaneous multi-train control

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A Multi-Objective Optimization-based Path Planning Method for Parallel Parking of Autonomous Vehicle via nonlinear programming 15

A Multi-Objective Optimization-based Path Planning Method fo...

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15th International Conference on Control, Automation, Robotics and Vision (ICARCV)

作者： Jing, Wei Feng, Dudong Zhang, Pinchao Zhang, Shijun Lin, Sihan Tang, Bowei Inst High Performance Comp Dept Comp Sci 1 Fusionopolis Way Singapore 138632 Singapore ASTAR Artificial Intelligence Initiat A AI 1 Fusionopolis Way Singapore 138632 Singapore Georgia Inst Technol Dept Mech Engn North Ave NW Atlanta GA 30332 USA Carnegie Mellon Univ Dept Civil & Environm Engn 5000 Forbes Ave Pittsburgh PA 15213 USA Carnegie Mellon Univ Dept Mech Engn 5000 Forbes Ave Pittsburgh PA 15213 USA

ISBN: (纸本)9781538695821

In recent years, Autonomous Vehicle has become highly desirable to improve efficiency of transportation, to reduce number of accidents and to reduce travelling cost. Among the common tasks in the autonomous driving system, parallel parking is one of the most important tasks, which is performed very frequently as a daily routine. Thus, planning an efficient path for parallel parking significantly helps to reduce the cost and improve the efficiency, which is of great interests at both academia and industry. In this paper, we propose a multi-objective optimization formulation and develop a nonlinear programming based method for the path planning problem of the parallel parking task. The proposed method is demonstrated to be able to solve the path planning problem for parallel parking efficiently and robustly with good optimization results as well as convergence property in the computational studies. We also conduct several analysis of the optimization algorithm to explain the impacts of the environmental parameters and the objectives in the multi-objective function.

关键词： Path Planning Autonomous Vehicle Multi-Objective Optimization nonlinear programming

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nonlinear programming-based ranging optimization for three-dimensional indoor time of arrival localization

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INTERNATIONAL JOURNAL OF DISTRIBUTED SENSOR NETWORKS 2017年第10期13卷 1-12页

作者： Sun, Jian Fu, Yongling He, Jie Li, Shengguang Fu, Jian Beihang Univ Sch Mech Engn & Automat Beijing 100191 Peoples R China FRI Minist Publ Secur Beijing Peoples R China Univ Sci & Technol Beijing Sch Comp & Commun Engn Beijing Peoples R China

The distribution of ranging errors of time of arrival techniques fails to satisfy zero means and equal variances. It is one of the major causations of position error of least square-based localization algorithm. The optimization of time of arrival ranging is defined as a nonlinear programming problem. Then, time of arrival ranging error model and geometric constraints are used to define the initial values, objective functions, and constraints of nonlinear programming, as well as to detect line of sight and nonline of sight. A three-dimensional localization algorithm of an indoor time of arrival-based positioning is proposed based on least square and the optimization algorithm. The performance of the ranging and localization accuracies is evaluated by simulation and field testing. Results show that the optimized ranging error successfully satisfies zero mean value and equal variances. Furthermore, the ranging and localization accuracies are significantly improved.

关键词： Time of arrival indoor positioning three-dimensional localization nonlinear programming least square

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A nonlinear programming approach to strategic planning of coal chemical industry with carbon constraints in China

A nonlinear programming approach to strategic planning of co...

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Applied Energy Symposium and Forum - Low-Carbon Cities and Urban Energy Systems (CUE)

作者： Huang, Yi Yi, Qun Kang, Jing-xian Wu, Guo-sheng Feng, Jie Xie, Ke-chang Li, Wen-ying Taiyuan Univ Technol Training Base State Key Lab Coal Sci & Technol Taiyuan 030024 Shanxi Peoples R China Chinese Acad Engn 2 BingJiaoKou HuTong Beijing 100088 Peoples R China

Coal chemical industry plays a critical role in China's economic growth and energy security. However, its carbon-intensity characteristics cause a large number of CO2 emissions during coal chemicals production. Facing intense pressure to reduce CO2 emissions, it is urgent to seek synergistic development between CO2 emissions reduction and coal chemical engineering. A nonlinear programming (NLP) approach is proposed to optimize the deployment of China's coal chemical industry under carbon constraints. The NLP model is pursuing the minimum CO2 emission per unit value of gross output of coal to chemicals sector (CPUVGC) with simultaneously satisfying economic growth. Twelve main categories coal chemical products and six measures or technologies of CO2 emission reduction are taken into consideration in the NLP model, based on which a short-term (2020), midterm (2030) and long-term (2050) deployment of coal chemical industry under restriction of CO2 emissions are investigated, and sensitivity or uncertainty analysis of effects of crude oil price (COP), which have a significant impact on coal chemicals price, on CO2 emission reduction target also is performed. Three scenarios involved 100% (positive), 50% (moderate) and 25% (conservative) of the predicted target of CO2 emissions reduction from different technologies or measures of CO2 emissions reduction are analyzed in different periods. At the end, the development roadmap (2020-2030-2050) of coal chemical industry under carbon constraints is plotted and some specific suggestions and safeguard measures are also provided to guarantee implement of the planning. Copyright 2018 Elsevier Ltd. All rights reserved.

关键词： Coal chemical industry in China CO2 emission nonlinear programming strategic planning Carbon constraints.

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Budget-Constrained Regression Model Selection Using Mixed Integer nonlinear programming

Budget-Constrained Regression Model Selection Using Mixed In...

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作者： Zhang, Jingying University of Arkansas

学位级别：Ph.D.

Regression analysis fits predictive models to data on a response variable and corresponding values for a set of explanatory variables. Often data on the explanatory variables come at a cost from commercial databases, so the available budget may limit which ones are used in the final model. In this dissertation, two budget-constrained regression models are proposed for continuous and categorical variables respectively using Mixed Integer nonlinear programming (MINLP) to choose the explanatory variables to be included in solutions. First, we propose a budget-constrained linear regression model for continuous response variables. Properties such as solvability and global optimality of the proposed MINLP are established, and a data transformation is shown to signicantly reduce needed big-Ms. Illustrative computational results on realistic retail store data sets indicate that the proposed MINLP outperforms the statistical software outputs in optimizing the objective function under a limit on the number of explanatory variables selected. Also our proposed MINLP is shown to be capable of selecting the optimal combination of explanatory variables under a budget limit covering cost of acquiring data sets. A budget-constrained and or count-constrained logistic regression MINLP model is also proposed for categorical response variables limited to two possible discrete values. Alternative transformations to reduce needed big-Ms are included to speed up the solving process. Computational results on realistic data sets indicate that the proposed optimization model is able to select the best choice for an exact number of explanatory variables in a modest amount of time, and these results frequently outperform standard heuristic methods in terms of minimizing the negative log-likelihood function. Results also show that the method can compute the best choice of explanatory variables affordable within a given budget. Further study adjusting the objective function to minimize the Bayesi

关键词： Budget Constraint Mixed Integer programming nonlinear programming Regression

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Convex nonlinear and Integer programming Approaches for Distributionally Robust Optimization of Complex Systems

Convex Nonlinear and Integer Programming Approaches for Dist...

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作者： Zhang, Yiling University of Michigan

学位级别：Ph.D.

The primary focus of the dissertation is to develop distributionally robust optimization (DRO) models and related solution approaches for decision making in energy and healthcare service systems with uncertainties, which often involves nonlinear constraints and discrete decision variables. Without assuming specific distributions, DRO techniques solve for solutions against the worst-case distribution of system uncertainties. In the DRO framework, we consider both risk-neutral (e.g., expectation) and risk-averse (e.g., chance constraint and Conditional Value-at-Risk (CVaR)) measures. The aim is twofold: i) developing efficient solution algorithms for DRO models with integer and/or binary variables, sometimes nonlinear structures and ii) revealing managerial insights of DRO models for specific applications. We mainly focus on DRO models of power system operations, appointment scheduling, and resource allocation in healthcare. Specifically, we first study stochastic optimal power flow (OPF), where (uncertain) renewable integration and load control are implemented to balance supply and (uncertain) demand in power grids. We propose a chance-constrained OPF (CC-OPF) model and investigate its DRO variant which is reformulated as a semidefinite programming (SDP) problem. We compare the DRO model with two benchmark models, in the IEEE 9-bus, 39-bus, and 118-bus systems with different flow congestion levels. The DRO approach yields a higher probability of satisfying the chance constraints and shorter solution time. It also better utilizes reserves at both generators and loads when the system has congested flows. Then we consider appointment scheduling under random service durations with given (fixed) appointment arrival order. We propose a DRO formulation and derive a conservative SDP reformulation. Furthermore, we study a scheduling variant under random no-shows of appointments and derive tractable reformulations for certain beliefs of no-show patterns. One preceding problem

关键词： Optimization under Uncertainty nonlinear programming Integer programming Chance-constrained Binary Programs Optimal Power Flow Appointment Scheduling Thesis

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