On a class of nonconvex problems where all local minima are global

Nonconvex All-Quadratic Global Optimization Problems:

On the Existence of Minima for Nonconvex Variational Problems

We consider the problem of minimizing autonomous, multiple integrals like

Deep linear neural networks with arbitrary loss: All local minima are global

We consider deep linear networks with arbitrary differentiable loss. We provide a short and elementary proof of the following fact: all local minima are global minima if each hidden layer is wider than either the input or output layer.

No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis

In this paper we develop a new framework that captures the common landscape underlying the common non-convex low-rank matrix problems including matrix sensing, matrix completion and robust PCA. In particular, we show for all above problems (including asymmetric cases): 1) all local minima are also globally optimal; 2) no highorder saddle points exists. These results explain why simple algorithm...

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...