opt.logarithmic_barrier.logarithmic_barrier_methods.primal_dual_feasible_init_point_method

primal_dual_feasible_init_point_method(f_B, x, t_B, mu, x_ast, p_ast, gf_B, Hf_B, plot=True, tol_inner_iter=1e-08, tol_outer_iter=1e-06, tol_backtracking=1e-12, max_inner_iter=30, max_total_iterations=30)

Outer iterations for logarithmic barrier method to numerically approximate solution of PL with only inequalities.

Parameters

• f_B (opt function class) – instance of class for f_B (logarithmic barrier).

• x (numpy ndarray) – initial point for logarithmic barrier method.

• t_B (float) – initial point for parameter barrier.

• mu (float) – parameter that will multiply barrier parameter.

• x_ast (numpy ndarray) – solution of min f_o subject to Ax <= b. It’s required that user knows the solution…

• p_ast (float) – value of f_B(x_ast).

• gf_B (opt function class) – instance of class for gradient of f_B (logarithmic barrier).

• Hf_B (opt function class) – instance of class for Hessian of f_B (logarithmic barrier).

• plot (bool) – if true make plots of Err vs iterations and plot of central path.

• tol_inner_iter (float) – tolerance that will halt method. Controls stopping criteria for inner iterations (iterations of descent method).

• tol_outer_iter (float) – tolerance that will halt method. Controls stopping criteria for outer iterations.

• tol_backtracking (float) – tolerance that will halt method. Controls value of line search by backtracking.

• max_inner_iter (int) – maximum number of inner iterations (iterations of descent method).

• max_total_iter (int) – maximum number of total iterations.

Returns

numpy array, approximation of x_ast.

total_iter (int): number of iterations regarding outer and

inner iterations.

t_B (float): updated barrier parameter.

x_plot_total_iter (numpy ndarray): numpy array that containts

in columns vector of approximations of all inner iterations. Last column contains x, approximation of solution. Useful for plotting.

Return type

x (numpy ndarray)