PREDICTOR–CORRECTOR SMOOTHING NEWTON METHOD FOR SOLVING SEMIDEFINITE PROGRAMMING

A Newton-CG Augmented Lagrangian Method for Semidefinite Programming

We consider a Newton-CG augmented Lagrangian method for solving semidefinite programming (SDP) problems from the perspective of approximate semismooth Newton methods. In order to analyze the rate of convergence of our proposed method, we characterize the Lipschitz continuity of the corresponding solution mapping at the origin. For the inner problems, we show that the positive definiteness of th...

A Recurrent Neural Network Model for Solving Linear Semidefinite Programming

In this paper we solve a wide rang of Semidefinite Programming (SDP) Problem by using Recurrent Neural Networks (RNNs). SDP is an important numerical tool for analysis and synthesis in systems and control theory. First we reformulate the problem to a linear programming problem, second we reformulate it to a first order system of ordinary differential equations. Then a recurrent neural network...

A Smoothing Newton Method for Semi-Infinite Programming

A Stochastic Smoothing Algorithm for Semidefinite Programming

We use rank one Gaussian perturbations to derive a smooth stochastic approximation of the maximum eigenvalue function. We then combine this smoothing result with an optimal smooth stochastic optimization algorithm to produce an efficient method for solving maximum eigenvalue minimization problems, and detail a variant of this stochastic algorithm with monotonic line search. Overall, compared to...

A Squared Smoothing Newton Method for Nonsmooth Matrix Equations and Its Applications in Semidefinite Optimization Problems

We study a smoothing Newton method for solving a nonsmooth matrix equation that includes semidefinite programming and the semidefinite complementarity problem as special cases. This method, if specialized for solving semidefinite programs, needs to solve only one linear system per iteration and achieves quadratic convergence under strict complementarity and nondegeneracy. We also establish quad...