MATLAB optimization toolbox

An implementation of this algorithm, using the sequential procedure within the MATLAB environment, was proposed by Figueroa and Romagnoli (1994). To solve step 2, the constr function from the MATLAB Optimization Toolbox has been used. The numerical integration necessary in this step has been performed via the function ode45 for the solution of ordinary differential equations. 

As mentioned earlier, the developed algorithm employs dynopt to solve the intermediate problems associated with the local interaction of the agents. Specifically, dynopt is a set of MATLAB functions that use the orthogonal collocation on finite elements method for the determination of optimal control trajectories. As inputs, this toolbox requires the dynamic process model, the objective function to be minimized, and the set of equality and inequality constraints. The dynamic model here is described by the set of ordinary differential equations and differential algebraic equations that represent the fermentation process model. For the purpose of optimization, the MATLAB Optimization Toolbox, particularly the constrained nonlinear rninimization routine fmincon [29], is employed. 

Branch MA, Grace A. MATLAB Optimization Toolbox User s Guide, The Math Works Inc., Natick, 1996. 

We use the Matlab software to calculate the value of m and w, according to the constraint condition (19). By using Matlab optimization toolbox to find the value of m and m, through maximum likelihood function. The calculation results are... 

Use the MATLAB Optimization Toolbox or Excel to determine the optimum values of temperature T(K) and flow rate Fb (L/h) that maximize the steady-state production rate of component B. The allowable values are 0 < < 200 and... 

The optimization problem presented in sections Robust Optimization Problem and Problem Definition is solved in this section. An SQP algorithm from the MATLAB optimization toolbox, coupled with a restart procedure, is employed for this purpose. Three variants of each analysis are presented, by varying parameter b in Eq. 2 (i) b = h/300, (i) b = h/400, and (iii) b = h/ 500, where h is the total height of the shear... 

Solution. Using the Optimization Toolbox from MATLAB, the BFGS method requires 20 iterations before the search is terminated, as shown below. 

If basic assumptions concerning the error structure are incorrect (e.g., non-Gaussian distribution) or cannot be specified, more robust estimation techniques may be necessary, e.g., Maria and Heinzle (1998). In addition to the above considerations, it is often important to introduce constraints on the estimated parameters (e.g., the parameters can only be positive). Such constraints are included in the simulation and parameter estimation package ACSL-OPTIMIZE and in the MATLAB Optimisation Toolbox. Because of numerical inaccuracy, scaling of parameters and data may be necessary if the numerical values are of greatly differing order. Plots of the residuals, difference between model and measurement value, are very useful in identifying systematic or model errors. 

In the MATLAB Statistics Toolbox, there are two functions for generating exact D-optimal designs, cordexch and rowexch. Both procedures are equivalent from the user s point of view. To use them, one must specify the number of variables, the number of the experiments, and the type of the desired regression model. Four different model choices are provided ... 

All the four PSO algorithms can find the global optimal solutions whereas the gradient based optimisation algorithm from the MATLAB Optimisation Toolbox, fminunc, fails to find the global optimal solutions when the initial values are not close to the global optimal solutions. 

Step 1 You can use the following MATLAB m-file along with the fsolve command (available in the Optimization Toolbox) ... 

Step 3 Call fsolve. Fsolve is in the optimization toolbox in MATLAB, which all versions do not have. 

As mentioned previously, quasi-Newton is the default non-linear optimization method included in Excel and Quattro-Pro, and is an option in the Professional Version of MathCad and in the Optimization Toolbox for Matlab. Various correction methods are made available in different packages. 

Grace, Optimization Toolbox for Use with Matlab, The MathWorks, Inc.. Natick, (1994). 

MATLAB in the Optimization Toolbox has the routine f solve. This routine implements an advanced version of the Newton-Raphson method as described above. However, rather than just a linear extrapolation, it implements a mixed quadratic and cubic extrapolation procedure. To learn more about this function, type... 

For carrying out Step 3, any parametrical optimization numerical method can be used. The optimization procedure (Agranovich, 2004) is realized using MATLAB functions dlqry , Kalman (Control System Toolbox) and finincon (Optimization Toolbox). 

As the MATLAB software packages with Optimisation Toolbox provides both effective ordinary differential equation (ODE) solvers as well as powerful optimization algorithms, the dynamic simulations reported in this paper are carried out by using the MATLAB Optimisation Toolbox (8). 

Birge, B. (2003). PSOt - a particle swarm optimization toolbox for use with Matlab. Swarm Intelligence Symposium, 2003. SIS 03. Proceedings of the 2003 IEEE. 

A short list of such tools is reported in Table 1, where GUI and MOO indicate, respectively, if the software has a Graphical User Interface and if it allows for multi-objective optimization. We also indicate if each tool is open-source and if it allows for customization of the optimization algorithms. We should note that we included in the table only multi-disciplinary optimization tools that are specifically based on CIO methods, while we excluded software based on classic techniques for convex optimization, integer linear/non-linear programming and methods addressing combinatorial optimization only. We also excluded those technical software products that are not devoted specifically to optimization but still may include optimization methods, such as Matlab (which provides the Optimization Toolbox), and other CAD/CAE or multi-physics software, as well as multi-disciplinary tools that provide (as an extra feature) one or more, often domain-specific, optimization techniques (see for instance AVL CAMEO [23]). 

Using the function of Ip - linear programming from the Optimization Toolbox Matlab, the matrix multi-step game manoeuvring mmg c program has been designed for the determination of the own ship safe trajectory in a collision situation. 

The mathematical model of FCC feed optimization described in section 9.2.3 was programmed in MATLAB model-files where the various constraints were formulated as objective components in the hard form. Applying the duality principle, the various maximization objectives were converted to minimization functions by simply negating them (Dantzig and Thapa, 1997 Deb, 2001). These model files were linked to the MOEA Toolbox to obtain the optimized values for the various control variables. LP was also applied and its solutions were used as a basis for comparison. 

For advanced techniques in modeling, identification, and control, MATLAB has a variety of additional toolboxes that are licensed individually. Relevant toolboxes for process control include control system, fuzzy logic, system identification, model predictive control, neural networks, optimization, partial differential equations, robust control, and statistics. 

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