https://datascienceschool.net/view-notebook/968c34fd6b404fcab12cbbbfd36418a2/ ================================================================================ * Optimization * output_data=function_A(input_data) * Find input_data which minimizes (or maximizes) output_data ================================================================================ * Grid search input_data_in_interval=cut_to_specific_range(large_input_data) for one_input_data in input_data_in_interval: output_data=function_A(one_input_data) is output_data is mimimum? break else: continue * Grid search takes much time when input variable has too many values ================================================================================ * Numerical optimization * It gets output from function, by using small number of calculation * Steepest gradient method * Newton method (upgraded from steepest gradient method) ================================================================================ * Optimization has "constraints" * Equality constraint - Input data should satisfy specific simultaneous equations (as constraint) * Inequality constraint - Input data should satisfy specific simultaneous inequalities (as constraint) ================================================================================ * How to solve optimization problem with equality constraint - Use Lagrange multiplier ================================================================================ * How to solve optimization problem with inequality constraint - Use KKT condition ================================================================================ Practical optimization problems - Linear programming (LP problem) - Quadratic programming (QP problem) ================================================================================