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Large-Scale Nonlinear Programming for Multi-scenario Optimization [chapter]

Carl D. Laird, Lorenz T. Biegler
2008 Modeling, Simulation and Optimization of Complex Processes  
Here we adapt the IPOPT barrier nonlinear programming algorithm to provide efficient parallel solution of multi-scenario problems.  ...  Here, we discuss the high level design principles of IPOPT 3.1 and develop a parallel Schur complement decomposition approach for large-scale multiscenario optimization problems.  ...  Introduction This study deals with development of specialized nonlinear programming algorithms for large, structured systems.  ... 
doi:10.1007/978-3-540-79409-7_22 dblp:conf/hpsc/LairdB06 fatcat:fven6sspvnbpfoaizkhl3tw2he

Optimal Design of Cryogenic Air Separation Columns Under Uncertainty [chapter]

Yu Zhu, Carl Laird
2009 Design for Energy and the Environment  
Nevertheless, this problem is solved efficiently using IPOPT, demonstrating the effectiveness of interior-point methods on complex, large-scale nonlinear programming problems.  ...  The multi-scenario approach is used to incorporate the uncertainty, giving rise to a nonlinear programming problem with over half a million variables.  ...  A multi-scenario approach is used to discretize the uncertainty space and formulate a large-scale nonlinear optimization problem.  ... 
doi:10.1201/9781439809136-c63 fatcat:3kqi4rkx2bdrzbmi5urd5vgalm

Optimal design of cryogenic air separation columns under uncertainty

Yu Zhu, Sean Legg, Carl D. Laird
2010 Computers and Chemical Engineering  
Nevertheless, this problem is solved efficiently using Ipopt, demonstrating the effectiveness of interior-point methods on complex, large-scale nonlinear programming problems.  ...  The multi-scenario approach is used to incorporate the uncertainty, giving rise to a nonlinear programming problem with over half a million variables.  ...  In this paper, we solve the large-scale multi-scenario programming problem using the nonlinear interior-point algorithm Ipopt (Wächter & Biegler, 2006) .  ... 
doi:10.1016/j.compchemeng.2010.02.007 fatcat:53n2pngaqjaoxlb3gvo4ywe77a

Interior-point decomposition approaches for parallel solution of large-scale nonlinear parameter estimation problems

Victor M. Zavala, Carl D. Laird, Lorenz T. Biegler
2008 Chemical Engineering Science  
Here we adapt the IPOPT barrier nonlinear programming algorithm to provide efficient parallel solution of multi-scenario problems.  ...  These large-scale problems lead to nonlinear programs (NLPs) with specialized structure that can be exploited by the NLP solver in order to obtained more efficient solutions.  ...  Introduction This study deals with the development of specialized nonlinear programming algorithms for large, structured optimization problems that arise in parameter estimation.  ... 
doi:10.1016/j.ces.2007.05.022 fatcat:om7bndcc6fegreqozkrz3mpot4

Implicit Mean-Variance Approach for Optimal Management of a Water Supply System under Uncertainty

Mashor Housh, Avi Ostfeld, Uri Shamir
2013 Journal of water resources planning and management  
the mean-variance tradeoff without the need to solve a large-scale problem.  ...  It utilizes the advantages of Implicit Stochastic Programming (ISP) to formulate a small size and easy to solve convex external optimization problem (quadratic objective and linear constraints) that generates  ...  need to solve large-scale optimization problems.  ... 
doi:10.1061/(asce)wr.1943-5452.0000307 fatcat:nxh4uymi2ja3pleudssp5axzki

A Review of Applications of Multiple-Criteria Decision-Making Techniques to Fisheries

1999 Marine Resource Economics  
Such nonlinearities are often intrinsic to the real-life problem. However, due to solution limitations of (large-scale) nonlinear models, linear approximations may be necessary.  ...  Nonlinear, Multi-objective Programming Most real-life problems exhibit some degree of nonlinearity.  ...  Goal programming and multi-attribute utility theory have been the most common forms of analysis used. Figure 1.  ... 
doi:10.1086/mre.14.1.42629251 fatcat:pigcyo73qzfx3igfanqnkik2bu

Optimization of Multi-Quality Water Networks: Can Simple Optimization Heuristics Compete with Nonlinear Solvers?

Mashor Housh
2021 Water  
The paper presents a simple optimization heuristic, which is specially tailored for the problem and compares its performance with a state-of-the-art nonlinear solver on large-scale systems.  ...  Then the final optimal solution is considered as the lowest objective value over the different runs. This will lead to a cumbersome and slow solution process for large-scale problems.  ...  ., [32] adopted a similar hybrid GA approach for solving large-scale nonlinear water management models. The proposed approach solves a linear program for each fitness evaluation.  ... 
doi:10.3390/w13162209 fatcat:5huymwntszdgzhb5xabq3cb4y4

A review of emerging techniques on generation expansion planning

Jinxiang Zhu, Mo-yuen Chow
1997 IEEE Transactions on Power Systems  
Since the computation revolution, there are several emerging techniques proposed to solve large scale optimization problem.  ...  Generation expansion planning is a challenging problem due to its large-scale, long-term, non-linear, and discrete nature of generation unit size.  ...  For a large-scale nonlinear integer programming GEP problem, it is much more difficult to solve by mathematical techniques directly.  ... 
doi:10.1109/59.627882 fatcat:xc72gevcfne5zbt6drik3d3e2a

Page 1312 of Mathematical Reviews Vol. , Issue 98B [page]

1998 Mathematical Reviews  
This algorithm is efficient for large-scale programs and can provide perfect scaling. The example discussed is encouraging. {For the entire collection see MR 97i:90006. } V. V. Kolbin (St.  ...  A primal-dual path-following algorithm is provided for linear and nonlinear programs of planning under uncertainty.  ... 

Combined Noncyclic Scheduling and Advanced Control for Continuous Chemical Processes

Damon Petersen, Logan Beal, Derek Prestwich, Sean Warnick, John Hedengren
2017 Processes  
A decomposition into nonlinear programming (NLP) dynamic optimization problems and mixed-integer linear programming (MILP) problems, without iterative alternation, allows for computationally light solution  ...  A novel formulation for combined scheduling and control of multi-product, continuous chemical processes is introduced in which nonlinear model predictive control (NMPC) and noncyclic continuous-time scheduling  ...  large-scale MINLP problem.  ... 
doi:10.3390/pr5040083 fatcat:6lt2sqkklfhqvn6d2ydmqisxqe

Methodology for Multi-stage, Operations- and Uncertainty-Aware Placement and Sizing of FACTS Devices in a Large Power Transmission System [article]

Vladimir Frolov, Michael Chertkov
2017 arXiv   pre-print
Non-linear, non-convex, multiple-scenario and multi-time-frame optimization is resolved via efficient heuristics, consisting of a sequence of alternating Linear Programmings or Quadratic Programmings (  ...  We develop new optimization methodology for planning installation of Flexible Alternating Current Transmission System (FACTS) devices of the parallel and shunt types into large power transmission systems  ...  was embedded in the large-scale optimization explicitly.  ... 
arXiv:1707.03686v1 fatcat:uacghe2bf5hhtnottmu4wpanhu

A decomposition-based solution method for stochastic mixed integer nonlinear programs

Maria Elena Bruni
2006 4OR  
It describes one of the very few existing implementations of a method for solving stochastic mixed integer nonlinear programming problems based on deterministic global optimization.  ...  In order to face the computational challenge involved in the solution of such multi-scenario nonconvex problems, a branch and bound approach is proposed that exploits the peculiar structure of stochastic  ...  Nevertheless, stochastic programming models remain amongst the more challenging optimization problems, because they can lead to very large scale problems.  ... 
doi:10.1007/s10288-006-0007-3 fatcat:jilwetdpdfg2dejjml3drmbpmq

Advances in mathematical programming models for enterprise-wide optimization

Ignacio E. Grossmann
2012 Computers and Chemical Engineering  
We first provide a brief overview of mathematical programming techniques (mixed-integer linear and nonlinear optimization methods), as well as decomposition methods, stochastic programming and modeling  ...  for remaining competitive in the global marketplace.  ...  and faster in large-scale problems.  ... 
doi:10.1016/j.compchemeng.2012.06.038 fatcat:jxycpmzmpfa37kp4jh3artwvaa

Risk management for a global supply chain planning under uncertainty: Models and algorithms

Fengqi You, John M. Wassick, Ignacio E. Grossmann
2009 AIChE Journal  
In addition, an algorithm based on the multi-cut L-shaped method is proposed to effectively solve the resulting large scale industrial size problems.  ...  We also introduce risk management models into the stochastic programming model, and multi-objective optimization schemes are implemented to establish the tradeoffs between cost and risk.  ...  This method is very effective for scenario reduction, particularly for large-scale problems.  ... 
doi:10.1002/aic.11721 fatcat:xlwaqjcu25empjwc652b2qbj7a

A Decomposition Method Based on SQP for a Class of Multistage Stochastic Nonlinear Programs

Xinwei Liu, Gongyun Zhao
2003 SIAM Journal on Optimization  
By using scenario analysis technique, a decomposition method based on SQP for solving a class of multi-stage stochastic nonlinear programs is proposed, which generates the search direction by solving parallelly  ...  Sequential quadratic programming methods are very effective for solving medium-size nonlinear programming.  ...  We would like to thank the associate editor and two anonymous referees for their valuable comments, which improved the paper largely.  ... 
doi:10.1137/s1052623402361447 fatcat:yfbnrpglwffsjnpezoiesxivli
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