Smoothing Sqp Algorithm for Non-lipschitz Optimization with Complexity Analysis

Smoothing Quadratic Regularization Methods for Box Constrained Non-lipschitz Optimization in Image Restoration

Abstract. We propose a smoothing quadratic regularization (SQR) method for solving box constrained optimization problems with a non-Lipschitz regularization term that includes the lp norm (0 < p < 1) of the gradient of the underlying image in the l2-lp problem as a special case. At each iteration of the SQR algorithm, a new iterate is generated by solving a strongly convex quadratic problem wit...

Using Modified IPSO-SQP Algorithm to Solve Nonlinear Time Optimal Bang-Bang Control Problem

In this paper, an intelligent-gradient based algorithm is proposed to solve time optimal bang-bang control problem. The proposed algorithm is a combination of an intelligent algorithm called improved particle swarm optimization algorithm (IPSO) in the first stage of optimization process together with a gradient-based algorithm called successive quadratic programming method (SQP) in the second s...

An effective optimization algorithm for locally nonconvex Lipschitz functions based on mollifier subgradients

Worst-Case Complexity of Smoothing Quadratic Regularization Methods for Non-Lipschitzian Optimization

Abstract. In this paper, we propose a smoothing quadratic regularization (SQR) algorithm for solving a class of nonsmooth nonconvex, perhaps even non-Lipschitzian minimization problems, which has wide applications in statistics and sparse reconstruction. The proposed SQR algorithm is a first order method. At each iteration, the SQR algorithm solves a strongly convex quadratic minimization probl...

PRISMA: PRoximal Iterative SMoothing Algorithm

Motivated by learning problems including max-norm regularized matrix completion and clustering, robust PCA and sparse inverse covariance selection, we propose a novel optimization algorithm for minimizing a convex objective which decomposes into three parts: a smooth part, a simple non-smooth Lipschitz part, and a simple non-smooth non-Lipschitz part. We use a time variant smoothing strategy th...