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Found 12 papers, 1 papers with code
A Newton-CG based augmented Lagrangian method for finding a second-order stationary point of nonconvex equality constrained optimization with complexity guarantees
In particular, we first propose a new Newton-CG method for finding an approximate SOSP of unconstrained optimization and show that it enjoys a substantially better complexity than the Newton-CG method [56].
Kurdyka-Łojasiewicz exponent via inf-projection
In addition, for nonconvex models, we show that the KL exponent of many difference-of-convex functions can be derived from that of their natural majorant functions, and the KL exponent of the Bregman envelope of a function is the same as that of the function itself.
A refined convergence analysis of pDCA$_e$ with applications to simultaneous sparse recovery and outlier detection
Moreover, for a large class of loss functions and regularizers, the KL exponent of the corresponding potential function are shown to be 1/2, which implies that the pDCA$_e$ is locally linearly convergent when applied to these problems.
Iteratively reweighted $\ell_1$ algorithms with extrapolation
Iteratively reweighted $\ell_1$ algorithm is a popular algorithm for solving a large class of optimization problems whose objective is the sum of a Lipschitz differentiable loss function and a possibly nonconvex sparsity inducing regularizer.
A successive difference-of-convex approximation method for a class of nonconvex nonsmooth optimization problems
We consider a class of nonconvex nonsmooth optimization problems whose objective is the sum of a smooth function and a finite number of nonnegative proper closed possibly nonsmooth functions (whose proximal mappings are easy to compute), some of which are further composed with linear maps.
A Non-monotone Alternating Updating Method for A Class of Matrix Factorization Problems
Finally, we conduct some numerical experiments using real datasets to compare our method with some existing efficient methods for non-negative matrix factorization and matrix completion.
Further properties of the forward-backward envelope with applications to difference-of-convex programming
In this paper, we further study the forward-backward envelope first introduced in [28] and [30] for problems whose objective is the sum of a proper closed convex function and a twice continuously differentiable possibly nonconvex function with Lipschitz continuous gradient.
Calculus of the exponent of Kurdyka-Łojasiewicz inequality and its applications to linear convergence of first-order methods
Since many existing local convergence rate analysis for first-order methods in the nonconvex scenario relies on the KL exponent, our results enable us to obtain explicit convergence rate for various first-order methods when they are applied to a large variety of practical optimization models.
Linear Convergence of Proximal Gradient Algorithm with Extrapolation for a Class of Nonconvex Nonsmooth Minimization Problems
In this paper, we study the proximal gradient algorithm with extrapolation for minimizing the sum of a Lipschitz differentiable function and a proper closed convex function.
Douglas-Rachford splitting for nonconvex optimization with application to nonconvex feasibility problems
We then apply our nonconvex DR splitting method to finding a point in the intersection of a closed convex set $C$ and a general closed set $D$ by minimizing the squared distance to $C$ subject to $D$.
Penalty methods for a class of non-Lipschitz optimization problems
We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid.
Global convergence of splitting methods for nonconvex composite optimization
In this paper, we examined two types of splitting methods for solving this nonconvex optimization problem: alternating direction method of multipliers and proximal gradient algorithm.
