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OMLT: Optimization Machine Learning Toolkit [article]

Francesco Ceccon, Jordan Jalving, Joshua Haddad, Alexander Thebelt, Calvin Tsay, Carl D. Laird, Ruth Misener
2022 arXiv   pre-print
The optimization and machine learning toolkit (OMLT) is an open-source software package incorporating neural network and gradient-boosted tree surrogate models, which have been trained using machine learning, into larger optimization problems. We discuss the advances in optimization technology that made OMLT possible and show how OMLT seamlessly integrates with the algebraic modeling language Pyomo. We demonstrate how to use OMLT for solving decision-making problems in both computer science and engineering.
arXiv:2202.02414v1 fatcat:b5o2qj3gj5b7nh5qvy5nem4xum

Scalable Preconditioning of Block-Structured Linear Algebra Systems using ADMM [article]

Jose S. Rodriguez, Carl D. Laird, Victor M. Zavala
2019 arXiv   pre-print
   D 1 J T 1 A T 1 J 1 . . . . . .  ...  D P J T P A T P J P B T 1 · · · B T P A 1 B 1 . . . . . .  ... 
arXiv:1904.11003v1 fatcat:fis24khdjja3xl5f252ywr6nse

Generalized Disjunctive Programming [chapter]

William E. Hart, Carl D. Laird, Jean-Paul Watson, David L. Woodruff, Gabriel A. Hackebeil, Bethany L. Nicholson, John D. Siirola
2017 Pyomo — Optimization Modeling in Python  
The set of available diameters (m) is: D = {.3048; .4064; Figure 1 : 1 a) Two Loop WDN. b) Hanoi WDN.  ...  D' Ambrosio et al. (2014) presented an MINLP model and Spatial Branch and Bound and piecewise linear relaxations were used.  ... 
doi:10.1007/978-3-319-58821-6_9 fatcat:rpfafu2hijgzldqwlsy7k7klpq

Clustering-based preconditioning for stochastic programs

Yankai Cao, Carl D. Laird, Victor M. Zavala
2015 Computational optimization and applications  
The corresponding costs are d g and d p . The generation levels in each scenario are given by g s with costs c g . The random demands are d s .  ...  The problem has the following structure: min d T g ∆g + d T p ∆p + S −1 s∈S c T g g s (39a) s.t.  ... 
doi:10.1007/s10589-015-9813-x fatcat:wkv5wkb2bnb23mues3xteycbze

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

Carl D. Laird, Lorenz T. Biegler
2008 Modeling, Simulation and Optimization of Complex Processes  
T q = −[(∇ xq L ℓ q ) T , (c ℓ q ) T , (D q x ℓ q −D q d ℓ ) T ], u T q = [∆x T q ∆λ T q ∆σ T q ], A T q = [ 0 0 −D T q ], W q =   H ℓ q +δ 1 I ∇ xq c ℓ q D T q (∇ xq c ℓ q ) T −δ 2 I 0 D q 0 −δ 2 I  ...  q∈Q f q (x q ) s.t . c q (x q ) = 0, S q x q ≥ 0, D q x q −D q d = 0    q ∈ Q (3) where x T q = [z T q y T q s T q d T q ] and the D q ,D q and S q matrices extract suitable components of the x q vector  ... 
doi:10.1007/978-3-540-79409-7_22 dblp:conf/hpsc/LairdB06 fatcat:fven6sspvnbpfoaizkhl3tw2he

Optimal design of cryogenic air separation columns under uncertainty

Yu Zhu, Sean Legg, Carl D. Laird
2010 Computers and Chemical Engineering  
, & Biegler, 2008; Zhu & Laird, 2008) .  ...  Multi-scenario programming approach The multi-scenario formulation can be expressed in general form as, min d,u,l P = f 0 (d) + k ∈ K q ∈ Q ω qk f qk (d, u k , l qk , Â v k , Â u q ) s.t. h qk (d, u k  ... 
doi:10.1016/j.compchemeng.2010.02.007 fatcat:53n2pngaqjaoxlb3gvo4ywe77a

Nonlinear programming strategies on high-performance computers

Jia Kang, Naiyuan Chiang, Carl D. Laird, Victor M. Zavala
2015 2015 54th IEEE Conference on Decision and Control (CDC)  
Thanks is also extended for partial financial support provided to Carl Laird by the National Science Foundation (CAREER Grant CBET# 0955205).  ...  We obtain −d T k g k = d T k W k (δ w )d k − c T k λ + k + 1 δ c (λ + k ) T λ + k , (I.8) where we use the second row of the augmented system to note that J k d k − 1 δc λ + k = −c k .  ...  In a first-order method, we update the duals λ 0 as λ + 0 = λ 0 + ∇ λ0 D(λ 0 ), (V.31) where ∇ λ0 D(λ 0 ) = p∈P Π p x p (V.32) is the gradient of D(λ 0 ).  ... 
doi:10.1109/cdc.2015.7402938 dblp:conf/cdc/KangCLZ15 fatcat:3tx4wnaeargflbzbpvmgubn2ka

A fast moving horizon estimation algorithm based on nonlinear programming sensitivity

Victor M. Zavala, Carl D. Laird, Lorenz T. Biegler
2008 Journal of Process Control  
The dynamic evolution of these states can be described by material balances around each plant unit, d (V k · ρ k · z k,j ) dt = F k z in k,j − F k z k,j z k,j (0) = z k,j 0 k = 1, ..., N U , j = 1, ...  ... 
doi:10.1016/j.jprocont.2008.06.003 fatcat:dadopdhlgfh7hdkczr4mpsv7za

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  
Eliminating Δν k from the resulting linear equation gives the primal-dual augmented system H k Δx k + ∇ x k c k Δλ k + D T k Δσ k = − ∇ x kL k ∇ x k c k Δx k = −c k D k Δx k −D k Δd = −D k x k +D k d ⎫  ...  Writing the Newton step for (12) at iteration leads to: ∇ x k x k L k Δx k + ∇ x k c k Δλ k + D T k Δσ k − S T k Δν k = −(∇ x k L k − S T k ν k ) ∇ x k c k Δx k = −c k D k Δx k −D k Δd = −D k x k +D  ... 
doi:10.1016/j.ces.2007.05.022 fatcat:om7bndcc6fegreqozkrz3mpot4

Fast implementations and rigorous models: Can both be accommodated in NMPC?

Victor M. Zavala, Carl D. Laird, Lorenz T. Biegler
2008 International Journal of Robust and Nonlinear Control  
Equation (10) shows the balance for the j-th component for every plant unit: d V ρw j dt = F w j in − F w j (10) where F is the mass flow rate (kg/h); V , equipment volume (m 3 ); t, time (s); ρ, gas  ... 
doi:10.1002/rnc.1250 fatcat:vl52vgx6kjg25j5iaorawr7x7a

An augmented Lagrangian interior-point approach for large-scale NLP problems on graphics processing units

Yankai Cao, Arpan Seth, Carl D. Laird
2016 Computers and Chemical Engineering  
The authors gratefully acknowledge the financial support provided to Yankai Cao and partial financial support provided to Carl Laird by the National Science Foundation (CAREER Grant CBET# 0955205).  ...  After solving equation (10) for d x k , the step in the multipliers d z k can be obtained using d z k = µ in X k −1 e − z k − Σ k d x k . (11) After the step directions are determined, the maximum step  ...  Compute the search direction 5.1 Solve (15) for d x k using the PCG method on GPU. . 5.2 Compute d z k from (11). .  ... 
doi:10.1016/j.compchemeng.2015.10.010 fatcat:ewljw6a7kzfmbfn5x2lom4sub4

An algorithmic framework for convex mixed integer nonlinear programs

Pierre Bonami, Lorenz T. Biegler, Andrew R. Conn, Gérard Cornuéjols, Ignacio E. Grossmann, Carl D. Laird, Jon Lee, Andrea Lodi, François Margot, Nicolas Sawaya, Andreas Wächter
2008 Discrete Optimization  
This paper is motivated by the fact that mixed integer nonlinear programming is an important and difficult area for which there is a need for developing new methods and software for solving large-scale problems. Moreover, both fundamental building blocks, namely mixed integer linear programming and nonlinear programming, have seen considerable and steady progress in recent years. Wishing to exploit expertise in these areas as well as on previous work in mixed integer nonlinear programming, this
more » ... work represents the first step in an ongoing and ambitious project within an open-source environment. COIN-OR is our chosen environment for the development of the optimization software. A class of hybrid algorithms, of which branch and bound and polyhedral outer approximation are the two extreme cases, is proposed and implemented. Computational results that demonstrate the effectiveness of this framework are reported, and a library of mixed integer nonlinear problems that exhibit convex continuous relaxations is made publicly available.
doi:10.1016/j.disopt.2006.10.011 fatcat:cd6osqzvkvhifov4o7t2ekyouu

Interior-Point Methods for Estimating Seasonal Parameters in Discrete-Time Infectious Disease Models

Daniel P. Word, James K. Young, Derek A. T. Cummings, Sopon Iamsirithaworn, Carl D. Laird, Danny Barash
2013 PLoS ONE  
t {I tz1 V t[T { ð6Þ I I tz1~b bzaĨ I t zS S t {Ñ N t V t[T { ð7Þ X i[Ty n t(t)~D T y D: ð8Þ Here, T y refers to the set of discrete time within a single year, n t(t) is a seasonally varying weight on  ...  Equation 8 ensures that the number of new susceptibles introduced into the population every year is equal to the number of reported births for each year, and DT y D is the cardinality of T y (i.e., the  ... 
doi:10.1371/journal.pone.0074208 pmid:24167542 pmcid:PMC3805536 fatcat:ojjh3n3pzfgqroguydbq5x57q4

Serotype Diversity and Reassortment between Human and Animal Rotavirus Strains: Implications for Rotavirus Vaccine Programs

Jon R. Gentsch, Ashley R. Laird, Brittany Bielfelt, Dixie D. Griffin, Krisztián Bányai, Madhu Ramachandran, Vivek Jain, Nigel A. Cunliffe, Osamu Nakagomi, Carl D. Kirkwood, Thea K. Fischer, Umesh D. Parashar (+3 others)
2005 Journal of Infectious Diseases  
The development of rotavirus vaccines that are based on heterotypic or serotype-specific immunity has prompted many countries to establish programs to assess the disease burden associated with rotavirus infection and the distribution of rotavirus strains. Strain surveillance helps to determine whether the most prevalent local strains are likely to be covered by the serotype antigens found in current vaccines. After introduction of a vaccine, this surveillance could detect which strains might
more » ... be covered by the vaccine. Almost 2 decades ago, studies demonstrated that 4 globally common rotavirus serotypes (G1-G4) represent 190% of the rotavirus strains in circulation. Subsequently, these 4 serotypes were used in the development of reassortant vaccines predicated on serotype-specific immunity. More recently, the application of reverse-transcription polymerase chain reaction genotyping, nucleotide sequencing, and antigenic characterization methods has confirmed the importance of the 4 globally common types, but a much greater strain diversity has also been identified (we now recognize strains with at least 42 P-G combinations). These studies also identified globally (G9) or regionally (G5, G8, and P2A[6]) common serotype antigens not covered by the reassortant vaccines that have undergone efficacy trials. The enormous diversity and capacity of human rotaviruses for change suggest that rotavirus vaccines must provide good heterotypic protection to be optimally effective. Globally, rotavirus infection is the most important cause of severe diarrhea in children. Most deaths occur in less-industrialized countries [1], and health organizations worldwide are promoting the development of rotavirus vaccines to help control this disease. The current strategy is based on the use of live, attenuated rotavirus vaccine candidates designed to elicit immunity comparable to that induced by natural rotavirus infections by providing homotypic or heterotypic protection against severe diarrhea caused by the major ro-
doi:10.1086/431499 pmid:16088798 fatcat:kvfdxp34gnbg3ltffgoabcwtcy

The IDAES Process Modeling Framework and Model Library – Flexibility for Process Simulation and Optimization

Andrew Lee, Jaffer H. Ghouse, John C. Eslick, Carl D. Laird, John D. Siirola, Miguel A. Zamarripa, Dan Gunter, John H. Shinn, Alexander W. Dowling, Debangsu Bhattacharyya, Lorenz T. Biegler, Anthony P. Burgard (+1 others)
2021 Journal of Advanced Manufacturing and Processing  
,r X r þ M p:i 8 p, i ð Þ ∈ I Â P Eqn 2 Element (mole basis only) X IÂP p,i ð Þ ∂ V ν e,i C p,i À Á ∂t ¼ X IÂP p,i ð Þ ν e,i F p,i,in À X IÂP p,i ð Þ ν e,i F p,i,out þ M e 8e ∈ E Eqn 3 reaction r.  ...  r α p,i,r X r,x þ LM p,i,x 8 p,i ð Þ ∈ I Â P Eqn 7 Element (mole basis only) L P IÂP p,i ð Þ ∂ Aν e,i C p,i,x ð Þ ∂t ¼ γν e,i P IÂP p,i ð Þ ∂F p,i,x ∂x þ LM e,x 8e ∈ E Eqn 8 Energy Balances Total Enthalpy  ... 
doi:10.1002/amp2.10095 fatcat:u2oiunyasrflpovgfvpla2w7w4
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