Yaguang Yang – Optimization Online

Combining Reinforcement Learning with Arc-search Interior-Point Method for Path Planning

Published: 2026/08/21

Yaguang Yang

Constrained Nonlinear Optimization, Control Applications, Nonlinear Optimization arc-search, nonlinear optimization, obstacle avoidance, Path planning

Path planning in environments containing obstacles has numerous practical applications. The problem is challenging because it is inherently nonlinear and nonconvex. Consequently, a variety of techniques have been developed to address this problem, among which machine learning and optimal control (or optimization) have emerged as two prominent approaches. In general, machine learning methods do not … Read more

An arc-search interior-point algorithm for nonlinear constrained optimization

Published: 2026/08/20

Yaguang Yang

Constrained Nonlinear Optimization, Nonlinear Optimization arc-search, Interior-point algorithm, nonlinear optimization

This paper proposes a new arc-search interior-point algorithm for the nonlinear constrained optimization problem. The proposed algorithm uses the second-order derivatives to construct a search arc that approaches the optimizer. Because the arc stays in the interior set longer than any straight line, it is expected that the scheme will generate a better new iterate … Read more

An Infeasible Interior-point Arc-search Algorithm for Nonlinear Constrained Optimization

Published: 2019/09/23

Constrained Nonlinear Optimization arc-search, constrained optimization, infeasible interior-point method, nonconvex optimization, nonlinear programming problems

In this paper, we propose an infeasible arc-search interior-point algorithm for solving nonlinear programming problems. Most algorithms based on interior-point methods are categorized as line search in the sense that they compute a next iterate on a straight line determined by a search direction which approximates the central path. The proposed arc-search interior-point algorithm uses … Read more

A Polynomial Arc-Search Interior-Point Algorithm for Linear Programming

Published: 2010/11/27

Yaguang Yang

Linear Programming arc-search, interior point methods, linear programming, polynomial algorithm

In this paper, ellipse is used to approximate the central path of the linear programming. An interior-point algorithm is devised to search the optimizers along the ellipse. The algorithm is proved to be polynomial with the complexity bound $O(n^{\frac{1}{2}}\log(1/\epsilon))$. Numerical test is conducted for problems in Netlib. For most tested Netlib problems, the result shows … Read more

A Polynomial Arc-Search Interior-Point Algorithm for Convex Quadratic Programming

Published: 2010/11/27

Yaguang Yang

Linear Programming arc-search, convex quadratic programming, polynomial algorithm

Arc-search is developed for linear programming in \cite{yang09, yang10}. The algorithms search for optimizers along an ellipse that are approximations of the central path. In this paper, the arc-search method is applied to primal-dual path-following interior-point method for convex quadratic programming. A simple algorithm with iteration complexity $O(\sqrt{n}\log(1/\epsilon))$ is devised. Several improvements on the simple … Read more

Arc-Search Path-Following Interior-Point Algorithms for Linear Programming

Published: 2009/08/14, Updated: 2009/09/19

Yaguang Yang

Linear Programming arc-search, linear programming, path following

Arc-search is developed in optimization algorithms. In this paper, simple analytic arcs are used to approximate the central path of the linear programming. The primal-dual path-following interior-point method is then used to search optimizers along the arcs for linear programming. They require fewer iterations to find the optimal solutions in all the tested problems in … Read more