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Found 23 papers, 2 papers with code
Newton-CG methods for nonconvex unconstrained optimization with Hölder continuous Hessian
In this paper we consider a nonconvex unconstrained optimization problem minimizing a twice differentiable objective function with H\"older continuous Hessian.
A Newton-CG based barrier-augmented Lagrangian method for general nonconvex conic optimization
In this paper we consider finding an approximate second-order stationary point (SOSP) of general nonconvex conic optimization that minimizes a twice differentiable function subject to nonlinear equality constraints and also a convex conic constraint.
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].
A first-order augmented Lagrangian method for constrained minimax optimization
In this paper we study a class of constrained minimax problems.
First-order penalty methods for bilevel optimization
Under suitable assumptions, an \emph{operation complexity} of $O(\varepsilon^{-4}\log\varepsilon^{-1})$ and $O(\varepsilon^{-7}\log\varepsilon^{-1})$, measured by their fundamental operations, is established for the proposed penalty methods for finding an $\varepsilon$-KKT solution of the unconstrained and constrained bilevel optimization problems, respectively.
A Newton-CG based barrier method for finding a second-order stationary point of nonconvex conic optimization with complexity guarantees
In this paper we consider finding an approximate second-order stationary point (SOSP) of nonconvex conic optimization that minimizes a twice differentiable function over the intersection of an affine subspace and a convex cone.
Accelerated first-order methods for convex optimization with locally Lipschitz continuous gradient
In particular, we first consider unconstrained convex optimization with LLCG and propose accelerated proximal gradient (APG) methods for solving it.
Primal-dual extrapolation methods for monotone inclusions under local Lipschitz continuity with applications to variational inequality, conic constrained saddle point, and convex conic optimization problems
In particular, we first propose a primal-dual extrapolation (PDE) method for solving a structured strongly MI problem by modifying the classical forward-backward splitting method by using a point and operator extrapolation technique, in which the parameters are adaptively updated by a backtracking line search scheme.
Stochastic Alternating Direction Method of Multipliers with Variance Reduction for Nonconvex Optimization
Specifically, the first class called the nonconvex stochastic variance reduced gradient ADMM (SVRG-ADMM), uses a multi-stage scheme to progressively reduce the variance of stochastic gradients.
Randomized block proximal damped Newton method for composite self-concordant minimization
The CSC minimization is the cornerstone of the path-following interior point methods for solving a broad class of convex optimization problems.
Generalized Conjugate Gradient Methods for $\ell_1$ Regularized Convex Quadratic Programming with Finite Convergence
In this paper we propose some generalized CG (GCG) methods for solving the $\ell_1$-regularized (possibly not strongly) convex QP that terminate at an optimal solution in a finite number of iterations.
Sparse Recovery via Partial Regularization: Models, Theory and Algorithms
Moreover, for a class of partial regularizers, any global minimizer of these models is a sparsest solution to the linear system.
Optimization over Sparse Symmetric Sets via a Nonmonotone Projected Gradient Method
For this problem, it is known that any accumulation point of the classical projected gradient (PG) method with a constant stepsize $1/L$ satisfies the $L$-stationarity optimality condition that was introduced in [3].
An Accelerated Proximal Coordinate Gradient Method
We develop an accelerated randomized proximal coordinate gradient (APCG) method, for solving a broad class of composite convex optimization problems.
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.
Orthogonal Rank-One Matrix Pursuit for Low Rank Matrix Completion
Numerical results show that our proposed algorithm is more efficient than competing algorithms while achieving similar or better prediction performance.
Schatten-$p$ Quasi-Norm Regularized Matrix Optimization via Iterative Reweighted Singular Value Minimization
In particular, we first introduce a class of first-order stationary points for them, and show that the first-order stationary points introduced in [11] for an SPQN regularized $vector$ minimization problem are equivalent to those of an SPQN regularized $matrix$ minimization reformulation.
A Randomized Nonmonotone Block Proximal Gradient Method for a Class of Structured Nonlinear Programming
When the problem under consideration is convex, we show that the expected objective values generated by RNBPG converge to the optimal value of the problem.
On the Complexity Analysis of Randomized Block-Coordinate Descent Methods
In this paper we analyze the randomized block-coordinate descent (RBCD) methods proposed in [8, 11] for minimizing the sum of a smooth convex function and a block-separable convex function.
A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems
A commonly used approach is the Multi-Stage (MS) convex relaxation (or DC programming), which relaxes the original non-convex problem to a sequence of convex problems.
Sequential Convex Programming Methods for A Class of Structured Nonlinear Programming
In this paper we study a broad class of structured nonlinear programming (SNLP) problems.
Fused Multiple Graphical Lasso
We expect the two brain networks for NC and MCI to share common structures but not to be identical to each other; similarly for the two brain networks for MCI and AD.
Penalty Decomposition Methods for Rank Minimization
In this paper we consider general rank minimization problems with rank appearing in either objective function or constraint.
