Fast Incremental Method for Nonconvex Optimization

An Efficient Neurodynamic Scheme for Solving a Class of Nonconvex Nonlinear Optimization Problems

‎By p-power (or partial p-power) transformation‎, ‎the Lagrangian function in nonconvex optimization problem becomes locally convex‎. ‎In this paper‎, ‎we present a neural network based on an NCP function for solving the nonconvex optimization problem‎. An important feature of this neural network is the one-to-one correspondence between its equilibria and KKT points of the nonconvex optimizatio...

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

An efficient improvement of the Newton method for solving nonconvex optimization problems

‎Newton method is one of the most famous numerical methods among the line search‎ ‎methods to minimize functions. ‎It is well known that the search direction and step length play important roles ‎in this class of methods to solve optimization problems. ‎In this investigation‎, ‎a new modification of the Newton method to solve ‎unconstrained optimization problems is presented‎. ‎The significant ...

A Distributed, Asynchronous and Incremental Algorithm for Nonconvex Optimization: An ADMM Based Approach

The alternating direction method of multipliers (ADMM) has been popular for solving many signal processing problems, convex or nonconvex. In this paper, we study an asynchronous implementation of the ADMM for solving a nonconvex nonsmooth optimization problem, whose objective is the sum of a number of component functions. The proposed algorithm allows the problem to be solved in a distributed, ...

Fast Stochastic Methods for Nonsmooth Nonconvex Optimization

We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem is very limited. For example, it is not known whether the proximal stochastic gradient method with constant minibatch converges to a stationary point. To tack...