optimization_in_scilab.pdf

# In the second chapter we present the qpsolve and

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In the second chapter we present the qpsolve and qp_solve functions which allows to solve quadratic problems. We describe the solvers which are used, the memory requirements and the internal design of the tool. The chapter 3 and 4 briefly present non-linear least squares problems and semidefinite pro- gramming. The chapter 5 focuses on genetic algorithms. We give a tutorial example of the optim_ga function in the case of the Rastrigin function. We also analyse the support functions which allow to configure the behavior of the algorithm and describe the algorithm which is used. 8

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The simulated annealing is presented in chapter 6, which gives an overview of the algorithm used in optim_sa . We present an example of use of this method and shows the convergence of the algorithm. Then we analyse the support functions and present the neighbor functions, the acceptance functions and the temperature laws. In the final section, we analyse the structure of the algorithm used in optim_sa . The LMITOOL module is presented in chapter 7. This tool allows to solve linear matrix inequalities. This chapter was written by Nikoukhah, Delebecque and Ghaoui. The syntax of the lmisolver function is analysed and several examples are analysed in depth. The chapter 8 focuses on optimization data files managed by Scilab, especially MPS and SIF files. Some optimization features are available in the form of toolboxes, the most important of which are the Quapro, CUTEr and the Unconstrained Optimization Problems toolboxes. These modules are presented in the chapter 9, along with other modules including the interface to CONMIN, to FSQP, to LIPSOL, to LPSOLVE, to NEWUOA. The chapter 10 is devoted to missing optimization features in Scilab. 9
Chapter 1 Non-linear optimization The goal of this chapter is to present the current features of the optim primitive Scilab. The optim primitive allows to optimize a problem with a nonlinear objective without constraints or with bound constraints. In this chapter, we describe both the internal design of the optim primitive. We analyse in detail the management of the cost function. The cost function and its gradient can be computed using a Scilab function, a C function or a Fortran 77 function. The linear algebra components are analysed, since they are used at many places in the algorithms. Since the management of memory is a crucial feature of optimization solvers, the current behaviour of Scilab with respect to memory is detailed here. Three non-linear solvers are connected to the optim primitive, namely, a BFGS Quasi-Newton solver, a L-BFGS solver, and a Non-Differentiable solver. In this chapter we analyse each solver and present the following features : the reference articles or reports, the author, the management of memory, the linear algebra system, especially the algorithm name and if dense/sparse cases are taken into account, the line search method.

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