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DRSOM: A DIMENSION REDUCED SECOND-ORDER METHOD

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arXiv 2022年

作者： Zhang, Chuwen Ge, Dongdong He, Chang Jiang, Bo Jiang, Yuntian Ye, Yinyu Shanghai University of Finance and Economics China Stanford University United States

In this paper, we propose a Dimension-Reduced Second-Order Method (DRSOM) for convex and nonconvex (unconstrained) optimization. Under a trust-region-like framework, our method preserves the convergence of the second-order method while using only curvature information in a few directions. Consequently, the computational overhead of our method remains comparable to the first-order such as the gradient descent method. Theoretically, we show that the method has a local quadratic convergence and a global convergence rate of O(∊−3/2) to satisfy the first-order and second-order conditions if the subspace satisfies a commonly adopted approximated Hessian assumption. We further show that this assumption can be removed if we perform a corrector step using a Krylov-like method periodically at the end stage of the algorithm. The applicability and performance of DRSOM are exhibited by various computational experiments, including L2 − Lp minimization, CUTEst problems, and sensor network localization. © 2022, CC BY-NC-ND.

关键词： nonlinear programming

Muwos - Multiple Use Water Optimization System for the Power Generation and Navigation Trade-Offs Analysis

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SSRN

SSRN 2022年

作者： de Figueiredo, Nelio Moura Blanco, Claudio José Cavalcante Campos Filho, Lúcio Carlos Pinheiro Mesquita, André Luiz Amarante Technological Institute Federal University of Pará PA Brazil Rua Augusto Correa 01 Belém PA Belém Brazil Technological Institute Federal University of Pará PA Brazil Rua Augusto Correa 01 PA Belém Belém Brazil Waterway and Port Research Group Faculty of Naval Engineering Federal University of Pará Rua Augusto Correa 01 PA Belém Brazil Amazon Development Center in Engineering Federal University of Pará NIDAE CAMTUC UFPA Av. Brasília S/N - Vila Permanente Tucuruí-PA 68455-901 Brazil

Reservoir operation is one of the major challenges in water resources planning and usually involves trading-off competing objectives. From the knowledge of the main water uses related to a hydro power plant, it is necessary to understand how energy uses impacts others and how energy use itself is impacted. Using the Tapajos River basin, Brazil, as a case study, this article aims to analyze water trade-offs between power generation and navigation uses, related to gains or losses of downstream water depth and of river convoy cargo capacity. The analysis of water conflicts was performed developing a nonlinear programming-based computational model called MUWOS (Multiple Use Water Optimization System), for conflict mitigation and minimization from the modeling and operational optimization of hydropower plants, for different navigation and hydrological scenarios. The result analysis showed that the main goals were achieved, evidencing that the research can aid the mitigating impacts process linked to hydro power projects for which navigation is an important economic aspect of the analyzed area. The method produced trade-off analyses and graphs, enabling verification of extent to which the prioritization of one use influences another use. The results obtained from the case study are consistent and useful for water management. © 2022, The Authors. All rights reserved.

关键词： nonlinear programming

Recent Developments in Security-Constrained AC Optimal Power Flow: Overview of Challenge 1 in the ARPA-E Grid Optimization Competition

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arXiv 2022年

作者： Aravena, Ignacio Molzahn, Daniel K. Zhang, Shixuan Petra, Cosmin G. Curtis, Frank E. Tu, Shenyinying Wächter, Andreas Wei, Ermin Wong, Elizabeth Gholami, Amin Sun, Kaizhao Sun, Xu Andy Elbert, Stephen T. Holzer, Jesse T. Veeramany, Arun Lawrence Livermore National Laboratory United States Georgia Institute of Technology United States Team Gollnlp United States Lehigh University United States Northwestern University United States University of California San Diego United States Team GO-SNIP Masachusetts Institute of Technology United States Team GMI-GO United States Pacific Northwest National Laboratory United States Grid Optimization Competition Organization Team

The optimal power flow problem is central to many tasks in the design and operation of electric power grids. This problem seeks the minimum cost operating point for an electric power grid while satisfying both engineering requirements and physical laws describing how power flows through the electric network. By additionally considering the possibility of component failures and using an accurate AC power flow model of the electric network, the security-constrained AC optimal power flow (SC-AC-OPF) problem is of paramount practical relevance. To assess recent progress in solution algorithms for SC-AC-OPF problems and spur new innovations, the U.S. Department of Energy’s Advanced Research Projects Agency–Energy (ARPA-E) organized Challenge 1 of the Grid Optimization (GO) competition. This special issue includes papers authored by the top three teams in Challenge 1 of the GO Competition (Teams gollnlp, GO-SNIP, and GMI-GO). To introduce these papers and provide context about the competition, this paper describes the SC-AC-OPF problem formulation used in the competition, overviews historical developments and the state of the art in SC-AC-OPF algorithms, discusses the competition, and summarizes the algorithms used by these three teams. © 2022, CC BY-SA.

关键词： nonlinear programming

Group-based control of large-scale micro-robot swarms with on-board Physical Finite-State Machines

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arXiv 2022年

作者： Li, Siyu Žefran, Miloš Paprotny, Igor The Department of Electrical and Computer Engineering University of Illinois Chicago ChicagoIL60607 United States

An important problem in microrobotics is how to control a large group of microrobots with a global control signal. This paper focuses on controlling a large-scale swarm of MicroStressBots with on-board physical finite-state machines. We introduce the concept of group-based control, which makes it possible to scale up the swarm size while reducing the complexity both of robot fabrication as well as swarm control. We prove that the group-based control system is locally accessible in terms of the robot positions. We further hypothesize based on extensive simulations that the system is globally controllable. A nonlinear optimization strategy is proposed to control the swarm by minimizing control effort. We also propose a probabilistically complete collision avoidance method that is suitable for online use. The paper concludes with an evaluation of the proposed methods in simulations. Copyright © 2022, The Authors. All rights reserved.

关键词： nonlinear programming

Joint Freeway Traffic State and Queue Profile Estimation Using Heterogeneous Data Sources: Differentiable programming Reformulation on a Layered Computational Graph

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SSRN

SSRN 2022年

作者： Lu, Jiawei Li, Chongnan Wu, Xin Zhou, Xuesong School of Sustainable Engineering The Built Environment Arizona State University TempeAZ85281 United States School of Traffic and Transportation Beijing Jiaotong University Beijing100044 China

This paper presents an integrated framework for joint traffic state and queue profile estimation (JSQE) on freeway corridors using heterogeneous data sources. The integrated modeling framework helps to fully utilize information from different components and take advantage of joint estimation spaces. On the other hand, potential inconsistencies between different modeling components should be recognized and carefully handled to ensure model feasibility. To minimize such inconsistencies, a nonlinear programming model is developed to formulate the JSQE problem by considering traffic flow models and observations from both corridor and local segment levels. At the corridor level, we use a fluid queue approximation to model queuing dynamics. Based on the assumption of polynomial arrival and departure rates, critical system variables such as time-dependent delay, travel time, and queue length are analytically derived. To maintain the differentiability of traffic state variables, we introduce continuous space-time distribution functions to model traffic flow variables and partial differential equations. A computational graph is constructed to represent the nonlinear programming model in a layered structure, which is then solved using a forwardbackward method. Extensive numerical experiments based on real-world and hypothetical datasets were designed to demonstrate the effectiveness of the proposed framework. © 2022, The Authors. All rights reserved.

关键词： nonlinear programming

Data-driven quadratic modeling in the Loewner framework from input-output time-domain measurements

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arXiv 2022年

作者： Karachalios, D.S. Gosea, I.V. Gkimisis, L. Antoulas, A.C. Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany Rice University Electrical and Computer Engineering Department HoustonTX77005 United States Baylor College of Medicine HoustonTX77030 United States

In this study, we present a purely data-driven method that uses the Loewner framework (LF) along with nonlinear optimization techniques to infer quadratic with affine control dynamical systems that admit Volterra series (VS) representations from input-output (i/o) time-domain measurements. The proposed method extensively employs optimization tools for interpolating the symmetric generalized frequency response functions (GFRFs) derived in the VS framework. The GFRF estimations are obtained from the Fourier spectrum (phase and amplitude) of the quasi-steady state system response under harmonic excitation. Appropriate treatment of these measurements under the developed framework allows the identification of low-order quadratic state-space models with non-trivial stable equilibria, such as in the Lorenz’63 forced system. We thus can achieve low-order global model identification for systems that can bifurcate to multiple equilibria after solely collecting measurements from a local stable operational regime. The developed framework is tested for several examples of increasing dimension and complexity, up to a test case of the viscous Burgers’ equation with Robin boundary conditions. In the latter case, this study enforces new directions of employing data-driven reduced model inference that successfully can provide low-order accurate surrogate predictive models suitable for control. Future directions and open challenges conclude this *** Codes 93B15, 93C15, 93C10, 65F45 © 2022, CC BY.

关键词： nonlinear programming

Variational Convexity of Functions and Variational Sufficiency in Optimization

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arXiv 2022年

作者： Khanh, Pham D.U.Y. Mordukhovich, Boris S. Phat, Vo Thanh Department of Mathematics HCMC University of Education Ho Chi Minh City Viet Nam Department of Mathematics Wayne State University DetroitMI United States aa1086wayne.edu

The paper is devoted to the study, characterizations, and applications of variational convexity of functions, the property that has been recently introduced by Rockafellar together with its strong counterpart. First we show that these variational properties of an extended-real-valued function are equivalent to, respectively, the conventional (local) convexity and strong convexity of its Moreau envelope. Then we derive new characterizations of both variational convexity and variational strong convexity of general functions via their second-order subdifferentials (generalized Hessians), which are coderivatives of subgradient mappings. We also study relationships of these notions with local minimizers and tilt-stable local minimizers. The obtained results are used for characterizing related notions of variational and strong variational sufficiency in composite optimization with applications to nonlinear programming. © 2022, CC0.

关键词： nonlinear programming

Muwos - Multiple Use Water Optimization System for the Power Generation and Navigation Trade-Offs Analysis

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SSRN

SSRN 2022年

作者： de Figueiredo, Nelio Moura Blanco, Claudio José Cavalcante Campos Filho, Lúcio Carlos Pinheiro Mesquita, André Luiz Amarante Technological Institute Federal University of Pará PA Brazil Rua Augusto Correa 01 Belém Brazil Technological Institute Federal University of Pará PA Brazil Rua Augusto Correa 01 Belém Brazil Waterway and Port Research Group Faculty of Naval Engineering Federal University of Pará Rua Augusto Correa 01 Belém Brazil Amazon Development Center in Engineering Federal University of Pará NIDAE CAMTUC UFPA Av. Brasília S/N - Vila Permanente Tucuruí-PA 68455-901 Brazil

关键词： nonlinear programming

Branch and price for submodular bin packing

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arXiv 2022年

作者： Xu, Liding D'Ambrosio, Claudia Vanier, Sonia Haddad Traversi, Emiliano LIX CNRS École Polytechnique Institut Polytechnique de Paris Palaiseau91128 France LIPN CNRS Université Sorbonne Paris Nord Villetaneuse93430 France

The Submodular Bin Packing (SMBP) problem asks for packing unsplittable items into a minimal number of bins for which the capacity utilization function is submodular. SMBP is equivalent to chance-constrained and robust bin packing problems under various conditions. SMBP is a hard binary nonlinear programming optimization problem. In this paper, we propose a branch-and-price algorithm to solve this problem. The resulting price subproblems are submodular knapsack problems, and we propose a tailored exact branch-and-cut algorithm based on a piece-wise linear relaxation to solve them. To speed up column generation, we develop a hybrid pricing strategy to replace the exact pricing algorithm with a fast pricing heuristic. We test our algorithms on instances generated as suggested in the literature. The computational results show the efficiency of our branch-and-price algorithm and the proposed pricing techniques. © 2022, CC BY-NC-ND.

关键词： nonlinear programming