Simple optimization toolbox for engineers

Summary form only given. Optimization problem is to find the best solution from all feasible solutions such as camera calibration[1], 3D reconstruction [2], visual odometry[3], human skeleton modeling. In order to find best solution, choosing an object function is very important. According to object function, the optimization problem could be distinguished with singular or multiple variable problem and linear or nonlinear optimization problem. If the optimization problem has special constraints except an object function, the problem is constrained optimization problem in contrast non-constrained optimization problem. In this video paper, simple optimization toolbox (SOT) is made to understand optimization method intuitively[3]. SOT deals with general unconstrained nonlinear optimization problem. SOT is written in interpreted language Matlab/Octave[4]. However, SOT GUI supports only Matlab. Various optimization methods are implemented in SOT such as gradient descent, newton, gradient descent based line search, newton based trust region, newton based trust region with saddle free[5], quasi newton, gauss newton and Levenberg-Marquardt. SOT provides simple examples to understand how to use the optimization method and engineering examples to show how to define and solve engineering problems: line search, scan matching and visual odometry[3]. And SOT supports visualization method such as plot and plot_x. By using theses functions, user could draw object functions and optimization process step by step easily. Figure 1 shows SOT GUI tool. Gradient descent based line search method is selected and test function is rosenbrock[3]. Goal position is (1, 1). User can observe the optimization sequence step by step using step button and modify parameters.