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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
MATLAB Optimization Toolbox includes a wide variety of methods for linear and nonlinear optimization on various platforms (Beck 2015). The MATLAB language facilitates problem input. Constraints and objective functions must be differentiable. TOMLAB is a modeling environment in MATLAB that has a unified input-output format and integrates automatic differentiation. It works with MATLAB solver algorithms as well as other solvers.
Relaxation schemes for mathematical programmes with switching constraints
Published in Optimization Methods and Software, 2021
Christian Kanzow, Patrick Mehlitz, Daniel Steck
The numerical experiments in this section were all done in MATLAB R2018a. The particular algorithms we use for our computations are the following: Schol: the adapted Scholtes relaxation scheme from Section 3,KanSch: the adapted Kanzow–Schwartz relaxation scheme from Section 4,SteUlb: the adapted Steffensen–Ulbrich relaxation scheme from Section 5.1, andSNOPT: the SNOPT nonlinear programming solver from [12], called through the TOMLAB programming environment.
Optimum reassignment of degrading components for non-repairable systems
Published in IISE Transactions, 2020
Xiaoyan Zhu, Yuqiang Fu, Tao Yuan
To apply model (19), component degradation-path function system structure and system failure mechanism need to be specified. For the general CRP, model (19) can be solved as the mixed binary nonlinear programming problem using commercial solvers, such as TOMLAB (Holmstr et al., 2010), which is a modeling and optimization environment in MATLAB.
Implementation of a goal programming framework for production and dyke material planning
Published in International Journal of Mining, Reclamation and Environment, 2018
Eugene Ben-Awuah, Hooman Askari-Nasab, Ahlam Maremi, Navid Seyed Hosseini
Both tailings management and solid waste management in terms of dyke construction planning are integrated in the proposed mathematical model. These are included in the objective function as a maximisation of NPV and minimisation of dyke construction costs. Mining panels (intersections of bench faces and pushbacks) are used as the units for controlling mining operations, while mining cuts (aggregated blocks) are used for controlling processing. The formulation and implementation of the MILGP model begins with considering its main subcomponents. The three basic subcomponents are: the objective function, the goal functions and the constraints. With the conceptual mining model, these components interact with the economic block model in an optimisation framework to achieve the objectives. The MILGP formulation development starts with identifying the appropriate numerical modelling platform that can be used in setting up the problem and solving it in a reasonable time. Matlab [31] is used as the numerical modelling platform and Tomlab/CPLEX [3] as the optimisation solver. This optimisation solver uses branch and cut algorithm and makes the solving of large-scale problems possible for the MILGP model. The generalised structure used by Tomlab/CPLEX in solving a MILP problem is identified and used as the basis for the numerical modelling of the MILGP formulation. With this in mind, Matlab is used in creating the numerical model of the three main subcomponent of the MILGP formulation to be passed on to Tomlab/CPLEX for optimisation. The user sets an optimisation termination criterion in CPLEX known as the gap tolerance (EPGAP). The EPGAP, which is a measure of optimality, sets an absolute tolerance on the gap between the best integer objective and the objective of the best node remaining in the branch and cut algorithm. It instructs CPLEX to terminate once a feasible integer solution within the set EPGAP has been found.