Yaguang Yang

A One-Factorization Predictor–Corrector Long-Step Arc-Search Method and a Curvature-Amplified Variant for Semidefinite Programming with a Homogeneous Self-Dual Embedding

Categories Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags ,

In a predictor-corrector arc-search method, a point on the predictor arc is first selected and a corrector is then computed at that point. Since the Karush-Kuhn-Tucker (KKT) matrix changes with the selected point, this correction may require a second factorization in each iteration. We propose a one-factorization arc-search method (OFAS) for semidefinite programming (SDP) that … Read more

An optimal orbit design for LISA

Categories Constrained Nonlinear Optimization, Multidisciplinary Design Optimization, Optimization of Systems modeled by PDEs Tags , ,

The ESA/NASA joint LISA (laser interferometer space antenna) mission is designed to detect gravitational waves to perform gravitational astronomy. A key mission requirement is the maintenance of a three-spacecraft constellation in a near-equilateral triangular configuration with a prescribed inter-spacecraft separation. Existing approaches have addressed this problem using simplified dynamical models to enhance tractability; however, the … Read more

ArcLP: A Matlab implementation of an O(√nL) arc-search infeasible interior-point algorithm for linear programming

Categories Linear Programming, Optimization Software and Modeling Systems Tags , ,

This paper presents a Matlab implementation of an arc-search infeasible interior point algorithm for linear programming (LP), which has a proven polynomial bound of O(√nL), the best among all interior-point algorithms for LP. Software architecture and major functions are discussed. Its ease of use is described by a simple example. Crucial strategies are summarized. Quality … Read more

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

Categories Constrained Nonlinear Optimization, Control Applications, Nonlinear Optimization Tags , , ,

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

Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , ,

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

Categories Constrained Nonlinear Optimization Tags , , , ,

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 Convex Quadratic Programming

Categories Linear Programming Tags , ,

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

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

Categories Linear Programming Tags , , ,

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

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

Categories Linear Programming Tags , ,

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