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We analyze the performance of a variant of Newton method with quadratic regularization for solving composite convex minimization problems. At each step of our method, we choose regularization parameter proportional to a certain power of the…
This paper considers the problem of unconstrained minimization of smooth convex functions having Lipschitz continuous gradients with known Lipschitz constant. We recently proposed an optimized gradient method (OGM) for this problem and…
This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity guarantees and practical performance. The method contains elements of two existing methods: the…
Based on the ideas of arXiv:1710.06612, we consider the problem of minimization of the Holder-continuous non-smooth functional $f$ with non-positive convex (generally, non-smooth) Lipschitz-continuous functional constraint. We propose some…
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. In…
This paper addresses the optimization problem of minimizing non-convex continuous functions, which is relevant in the context of high-dimensional machine learning applications characterized by over-parametrization. We analyze a randomized…
Adaptive cubic regularization methods for solving nonconvex problems need the efficient computation of the trial step, involving the minimization of a cubic model. We propose a new approach in which this model is minimized in a low…
We propose a new first-order method for minimizing nonconvex functions with a Lipschitz continuous gradient and Hessian. The proposed method is an accelerated gradient descent with two restart mechanisms and finds a solution where the…
We propose a descent subgradient algorithm for minimizing a real function, assumed to be locally Lipschitz, but not necessarily smooth or convex. To find an effective descent direction, the Goldstein subdifferential is approximated through…
We study the composite convex optimization problems with a Quasi-Self-Concordant smooth component. This problem class naturally interpolates between classic Self-Concordant functions and functions with Lipschitz continuous Hessian.…
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This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their…
The paper is devoted to new modifications of recently proposed adaptive methods of Mirror Descent for convex minimization problems in the case of several convex functional constraints. Methods for problems of two classes are considered. The…
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In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
In this paper, a descent method for nonsmooth multiobjective optimization problems on complete Riemannian manifolds is proposed. The objective functions are only assumed to be locally Lipschitz continuous instead of convexity used in…
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…
Many practical optimization problems involve objective function values that are corrupted by unavoidable numerical errors. In smooth nonconvex optimization, quasi-Newton methods combined with line search are widely used due to their…
We consider minimization of a smooth nonconvex objective function using an iterative algorithm based on Newton's method and the linear conjugate gradient algorithm, with explicit detection and use of negative curvature directions for the…