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Nonlinear Optimization
Published in Michael W. Carter, Camille C. Price, Ghaith Rabadi, Operations Research, 2018
Michael W. Carter, Camille C. Price, Ghaith Rabadi
MINOS is one of several linear and nonlinear optimizers offered within the AIMMS, APMonitor, GAMS, TOMLAB, and AMPL modeling systems and the NEOS Server, but it also can be used as a stand-alone package. The MINOS system is a general-purpose optimizer, designed to find locally optimal solutions involving smooth nonlinear objective and constraint functions. It takes advantage of sparsity in the constraint set, is economical in its use of storage for the reduced Hessian approximation, and is capable of solving large-scale linear and nonlinear programs.
Delay Tolerant Monitoring of Mobility-Assisted WSN
Published in Athanasios Vasilakos, Yan Zhang, Thrasyvoulos V. Spyropoulos, Delay Tolerant Networks: Protocols and Applications, 2016
Abdelmajid Khelil, Faisal Karim Shaikh, Azad Ali, Neeraj Suri, Christian Reinl
For the proof of concept, the proposed algorithm in Section 7.4.3.2 has been designed and tested for the representative scenarios discussed in Figure 7.2. We solved STEP 1 using the IPOPT [9] NLP-solver on the NEOS server [8]. The MILP STEP 2 was solved by using CPLEX [14] running on a PC (Intel R
A new interior-point approach for large separable convex quadratic two-stage stochastic problems
Published in Optimization Methods and Software, 2022
Jordi Castro, Paula de la Lama-Zubirán
In addition to the CPLEX general purpose solver, we explored other specialized methods for two-stage stochastic problems, namely: Benders decomposition, and Benders decomposition with regularization by the level set method, as implemented in the FortSP stochastic solver [32]; the primal-dual column generation approach of [18]; and the dual decomposition approach (with an interior-point cutting-plane generator) implemented in the DSP (Decomposition for Structured Programming) stochastic solver [21]. Comparing BlockIP with these other approaches is not straightforward since: the solvers of [18,32] are not freely available; the DSP solver had to be used remotely from the Neos Server [12] (we did not succeed in installing it locally due to its many dependencies with third-party software); and the four hardwares (i.e. those of [18,32], the Neos Server, and our work) were different, so only an indirect comparison can be performed.
Multi-objective two-stage stochastic programming for adaptive interdisciplinary pain management with piecewise linear network transition models
Published in IISE Transactions on Healthcare Systems Engineering, 2021
Gazi Md Daud Iqbal, Jay Rosenberger, Victoria Chen, Robert Gatchel, Carl Noe
The data set used in this research is from the Eugene McDermott Center for Pain Management at UT Southwestern Medical Center. It has 294 observations, which means 294 patients completed both stage 1 and stage 2. The data are divided into training and testing datasets consisting of 235 and 59 observations, respectively. The data set consists of 62 state variables, 5 mid-pain outcomes, 5 post-pain outcomes, 14 stage 1 decision variables, and 13 stage 2 decision variables. In stage 1, there are 8 pharmaceutical treatment variables and 6 procedural treatment variables, while in stage 2, there are 8 pharmaceutical variables and 5 procedural variables. In Appendix A, we describe these treatment variables in more detail. Procedural variables are binary, while pharmaceutical variables are discrete. We use PDA, OSW, BDI, SF-36 PCS, and SF-36 MCS pain outcomes in this optimization model as described in section 1.2. We use a two-stage feature selection method to find optimal features (Rawat & Manry, 2017). We solve the optimization problem to determine treatment policy, and we compare the treatment policy with observed data and policies found in the S-L2SP model. We code all math optimization models in the AMPL modeling language, and we use IBM ILOG CPLEX 12.7.0.0 to solve the M-L2SP model on a NEOS server (Dolan, 2001; Gropp & Moré, 1997; Czyzyk et al., 1998) with the number of threads equal to 1. The program terminates if a relative tolerance on the gap between the best integer objective and the objective of the best node remaining are within 0.01.
Two-stage stochastic programming for interdisciplinary pain management
Published in IISE Transactions on Healthcare Systems Engineering, 2019
Na Wang, Jay Rosenberger, Gazi Md Daud Iqbal, Victoria Chen, Robert J Gatchel, Carl Noe, Aera Kim LeBoulluec
We describe the determination of the sample size and treatment coefficient in more detail in this section. We coded all procedures in the AMPL modeling language, and we used IBM ILOG CPLEX 12.7.0.0 to solve L2SP on the NEOS server (Gropp and Moré, 1997; Czyzyk et al. 1998; Dolan, 2001) with the number of threads equal to 1. The program terminates if a relative tolerance on the gap between the best integer objective and the objective of the best node remaining are within 0.01.