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19th Annual International Conference on Computational Science (ICCS)

作者： De Marchi, Alberto Gerdts, Matthias Bundeswehr Univ Munich Dept Aerosp Engn Werner Heisenberg Weg 39 D-85577 Neubiberg Germany

ISBN: (纸本)9783030227449;9783030227432

We investigate real asymmetric linear systems arising in the search direction generation in a nonsmooth Newton's method. This applies to constrained optimisation problems via reformulation of the necessary conditions into an equivalent nonlinear and nonsmooth system of equations. We propose a strategy to exploit the problem structure. First, based on the sub-blocks of the original matrix, some variables are selected and ruled out for a posteriori recovering;then, a smaller and symmetric linear system is generated;eventually, from the solution of the latter, the remaining variables are obtained. We prove the method is applicable if the original linear system is well-posed. We propose and discuss different selection strategies. Finally, numerical examples are presented to compare this method with the direct approach without exploitation, for full and sparse matrices, in a wide range of problem size.

关键词： structure exploitation Linear algebra Nonsmooth Newton's method Nonlinear optimization

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structure exploitation in an Interior-Point Method for Fully Discretized, State Constrained Optimal Control Problems

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VIETNAM JOURNAL OF MATHEMATICS 2018年第4期46卷 1089-1113页

作者： Huber, Andreas Gerdts, Matthias Bertolazzi, Enrico Bundeswehr Univ Munich Werner Heisenberg Weg 39 D-85577 Neubiberg Germany Univ Trento Via Sommar 9 I-38123 Trento Italy

We discuss a direct discretization method for state-constrained optimal control problems and an interior-point method, which is used to solve the resulting large-scale and sparse nonlinear optimization problems. The main focus of the paper is on the investigation of an efficient method to solve the occurring linear equations with saddle-point structure. To this end, we exploit the particular structure that arises from the optimal control problem and the discretization scheme and use a tailored linear algebra solver ALGLIN in combination with a re-ordering of the saddle-point matrices. Numerical experiments for a simple optimal control problem show a significant speed-up compared to state-of-the-art sparse LU decomposition methods like MA57 or MUMPS in combination with IPOPT.

关键词： Optimal control Direct discretization method Interior-point method structure exploitation

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Determinants of M&A acquisition premium: a social capital perspective

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COMPETITIVENESS REVIEW 2022年第2期32卷 214-229页

作者： Nguyen, Huy Will Zhu, Zhu Jung, Young Hoon Kim, Dong Shin Montclair State Univ Dept Management Montclair NJ 07043 USA Univ Texas Dallas Naveen Jindal Sch Management Richardson TX 75083 USA

Purpose What determines the level of acquisition premium? This paper aims to investigate the effect of acquirers' social capital as reflected through their network position (structural holes and network density) on the level of acquisition premiums. Design/methodology/approach This study predicts acquisition premiums using a panel data set of 324 mergers and acquisition (M&A) transactions including 161 unique acquirers over a 21-year timeframe. M&A and alliance information are obtained from the securities data company platinum database;firm financial data are obtained from the COMPUSTAT database. Findings The results show that alliance network social capital provides acquiring firms with information benefits, thus, reducing the acquisition premium. However, such information benefits are also contingent on target valuation uncertainty and acquirers' structure exploitation tendency. Practical implications Different types of network structures provide different social capital influences: managers should be aware of their advantages and pitfalls when engaging in M&As. The findings suggest that firms should pay close attention to social capital when making decisions regarding acquisition premiums. Originality/value Past research has indicated that acquiring firms tend to overestimate the value of target firms. Still, little attention has been paid to organizational-level social capital in analyzing the determinants of acquisition premiums. This study offers insight into the effect of network structure on M&A acquisition premiums.

关键词： Social capital Alliances Acquisition premium structure exploitation

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NUMERICAL structure OF THE HESSIAN OF THE LAGRANGE DUAL FUNCTION FOR A CLASS OF CONVEX PROBLEMS

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2017年第1期55卷 574-593页

作者： Klintberg, Emil Gros, Sebastien Chalmers Univ Technol Signals & Syst Gothenburg Sweden

This paper considers a structured separable convex optimization problem, motivated by the deployment of model predictive control on multiagent systems that are interacting via nondelayed couplings. We show that the dual decomposition of this problem yields a numerical structure in the Hessian of the dual function. This numerical structure allows for deploying a quasi Newton method in the dual space. For large problems, this approach yields a large reduction of the computational complexity of solving the problem, and for geographically distributed problems a reduction in the communication burden.

关键词： dual decomposition Newton method structure exploitation dual Hessian

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A parallel quadratic programming method for dynamic optimization problems

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MATHEMATICAL PROGRAMMING COMPUTATION 2015年第3期7卷 289-329页

作者： Frasch, Janick V. Sager, Sebastian Diehl, Moritz Univ Magdeburg Inst Math Optimizat Magdeburg Germany Univ Freiburg Dept Microsyst Engn Freiburg Germany

Quadratic programming problems (QPs) that arise from dynamic optimization problems typically exhibit a very particular structure. We address the ubiquitous case where these QPs are strictly convex and propose a dual Newton strategy that exploits the block-bandedness similarly to an interior-point method. Still, the proposed method features warmstarting capabilities of active-set methods. We give details for an efficient implementation, including tailored numerical linear algebra, step size computation, parallelization, and infeasibility handling. We prove convergence of the algorithm for the considered problem class. A numerical study based on the open-source implementation qpDUNES shows that the algorithm outperforms both well-established general purpose QP solvers as well as state-of-the-art tailored control QP solvers significantly on the considered benchmark problems.

关键词： Quadratic programming Dual decomposition Model predictive control structure exploitation Parallel algorithms

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Production Optimization – Facilitated by Divide and Conquer Strategies

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IFAC-PapersOnLine 2015年第6期48卷 1-8页

作者： Bjarne Foss Bjarne Grimstad Vidar Gunnerud Department of Engineering Cybernetics NTNU Solution Seeker AS

This paper explores the use of divide and conquer algorithms to solve production optimization problems. exploitation of inherent structure facilitates efficient formulations and solutions to production optimization problems that frequently appear in the upstream oil and gas sector. We present the daily production optimization, which gives rise to network optimization problems, and also add some comments to the closely linked reservoir optimization problem. Subsequently, a common non-invasive optimization approach is presented prior to three concepts that apply decomposition and structure exploitation. The first approach splits a network simulator into interconnected parts and exploits the local components and their couplings in devising efficient formulations and algorithms. This opens for a range of opportunities in terms of formulations and algorithms, several of which will be discussed. This part is accompanied by a realistic numerical study. The second approach exploits a decomposable network structure, which frequently appears in large production systems, by applying a Lagrangian type decomposition. The last approach deals with reservoir optimization where there is no apparent structure to exploit. However, by recognizing this as a dynamic optimization problem, it may be split in the time domain. The paper ends with some conclusions.

关键词： production optimization reservoir optimization formulations decomposition structure exploitation optimization

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A simultaneous approach for calibrating Rate Based Models of packed distillation columns based on multiple experiments

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CHEMICAL ENGINEERING SCIENCE 2013年 104卷 228-232页

作者： Bonilla, J. Logist, F. Huyck, B. Degreve, J. De Moor, B. Van Impe, J. Katholieke Univ Leuven Dept Chem Engn CIT BioTeC B-3001 Louvain Belgium Katholieke Univ Leuven Dept Elect Engn ESAT SCD B-3001 Louvain Belgium

This paper presents the calibration of a steady state Rate Based Model (RBM) for distillation based on multiple experiments. A packed column is considered, using non-equilibrium stages to represent the packing segments. For an efficient and accurate calibration, the number of model equations and parameters is first reduced via analytical manipulations and a sensitivity analysis. Second, the model is formulated such that a sparse and banded Jacobian can be exploited. Finally, novel constraints on the physical parameters are derived such that the parameter estimation yields consistent results. The model prediction capabilities are successfully validated with experimental data. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Distillation Packed columns Parameter estimation Nonlinear programming structure exploitation Simultaneous estimation

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Efficient NMPC for nonlinear models with linear subsystems

Efficient NMPC for nonlinear models with linear subsystems

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52nd IEEE Annual Conference on Decision and Control (CDC)

作者： Quirynen, Rien Gros, Sehastien Diehl, Moritz Katholieke Univ Leuven OPTEC B-3001 Leuven Heverlee Belgium

ISBN: (纸本)9781467357173

Real-time optimal control algorithms for fast, mechatronic systems need to be run on embedded hardware and they need to respect tight timing constraints. When using nonlinear models, the simulation and generation of sensitivities forms a computationally demanding part of any algorithm. Automatic code generation of Implicit Runge-Kutta (IRK) methods has been shown to reduce its CPU time significantly. However, a typical model also shows a lot of structure that can be exploited in a rather elegant and efficient way. The focus of this paper is on nonlinear models with linear subsystems. With the proposed model formulation, the new auto generated integrators can be considered a powerful generalization of other solvers, e.g. those that support quadrature variables. A speedup of up to 5 - 10 is shown in the integration time for two examples from the literature.

关键词： structure exploitation code generation IRK methods NMPC embedded optimization

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Efficient NMPC for nonlinear models with linear subsystems

Efficient NMPC for nonlinear models with linear subsystems

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IEEE Annual Conference on Decision and Control

作者： Rien Quirynen Sebastien Gros Moritz Diehl Optimization in Engineering Center (OPTEC) KU Leuven Kasteelpark Arenberg 10 B-3001 Leuven-Heverlee Belgium

ISBN: (纸本)9781467357159

Real-time optimal control algorithms for fast, mechatronic systems need to be run on embedded hardware and they need to respect tight timing constraints. When using nonlinear models, the simulation and generation of sensitivities forms a computationally demanding part of any algorithm. Automatic code generation of Implicit Runge-Kutta (IRK) methods has been shown to reduce its CPU time significantly. However, a typical model also shows a lot of structure that can be exploited in a rather elegant and efficient way. The focus of this paper is on nonlinear models with linear subsystems. With the proposed model formulation, the new auto generated integrators can be considered a powerful generalization of other solvers, e.g. those that support quadrature variables. A speedup of up to 5-10 is shown in the integration time for two examples from the literature.

关键词： structure exploitation code generation IRK methods NMPC embedded optimization Code generation Nonlinear Models INTEGRATION TIME SUB-SYSTEM embedded hardware Time constraints CPU time

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A reduced order rate based model for distillation in packed columns: Dynamic simulation and the differentiation index problem

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CHEMICAL ENGINEERING SCIENCE 2012年第1期68卷 401-412页

作者： Bonilla, J. Logist, F. Degreve, J. De Moor, B. Van Impe, J. Katholieke Univ Leuven Dept Chem Engn CIT BioTEC B-3001 Louvain Belgium Katholieke Univ Leuven Dept Elect Engn ESAT SCD B-3001 Louvain Belgium

This paper presents a rigorous dynamic rate based model suitable for simulation of distillation of mixtures in packed columns. The model equations are described in detail considering structure exploitation at simulation level in order to alleviate the large number of states involved in the model description. Moreover, this kind of model may leads to differential-algebraic equations with a differentiation index higher than one. Here this issue is analyzed and a differentiation-index reduction procedure based on the incidence of model states in the Jacobian and the properties of the model dynamics is proposed. This procedure allows for a simplified index-1 model with a reduced stiffness so that dynamic simulation can be performed with off-the-shelf solvers. (C) 2011 Published by Elsevier Ltd.

关键词： Distillation Mathematical modeling Model reduction Dynamic simulation structure exploitation High-index DAE

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