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Bregman dynamics, contact transformations and convex optimization
Recent research on accelerated gradient methods of use in optimization has demonstrated that these methods can be derived as discretizations of...
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Unified Analysis of Stochastic Gradient Methods for Composite Convex and Smooth Optimization
We present a unified theorem for the convergence analysis of stochastic gradient algorithms for minimizing a smooth and convex loss plus a convex...
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Conditions for linear convergence of the gradient method for non-convex optimization
In this paper, we derive a new linear convergence rate for the gradient method with fixed step lengths for non-convex smooth optimization problems...
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Linearized Proximal Algorithms with Adaptive Stepsizes for Convex Composite Optimization with Applications
We propose an inexact linearized proximal algorithm with an adaptive stepsize, together with its globalized version based on the backtracking...
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Oracle Complexity Separation in Convex Optimization
Many convex optimization problems have structured objective functions written as a sum of functions with different oracle types (e.g., full gradient,...
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A simple method for convex optimization in the oracle model
We give a simple and natural method for computing approximately optimal solutions for minimizing a convex function f over a convex set K given by a...
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A graph-based decomposition method for convex quadratic optimization with indicators
In this paper, we consider convex quadratic optimization problems with indicator variables when the matrix Q defining the quadratic term in the...
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Complexity bound of trust-region methods for convex smooth unconstrained multiobjective optimization
In this paper, we analyze the worst-case complexity of trust-region methods for solving unconstrained smooth multiobjective optimization problems. We...
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Convex and concave envelopes of artificial neural network activation functions for deterministic global optimization
In this work, we present general methods to construct convex/concave relaxations of the activation functions that are commonly chosen for artificial...
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Regrets of proximal method of multipliers for online non-convex optimization with long term constraints
The online optimization problem with non-convex loss functions over a closed convex set, coupled with a set of inequality (possibly non-convex)...
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Duality for convex infinite optimization on linear spaces
This note establishes a limiting formula for the conic Lagrangian dual of a convex infinite optimization problem, correcting the classical version of...
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Recent Theoretical Advances in Non-Convex Optimization
Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and...
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The augmented Lagrangian method can approximately solve convex optimization with least constraint violation
There are many important practical optimization problems whose feasible regions are not known to be nonempty or not, and optimizers of the objective...
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On the Parallelization Upper Bound for Asynchronous Stochastic Gradients Descent in Non-convex Optimization
In deep learning, asynchronous parallel stochastic gradient descent (APSGD) is a broadly used algorithm to speed up the training process. In...
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Convex Analysis on Hadamard Spaces and Scaling Problems
In this paper, we address the bounded/unbounded determination of geodesically convex optimization on Hadamard spaces. In Euclidean convex...
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A fast continuous time approach for non-smooth convex optimization using Tikhonov regularization technique
In this paper we would like to address the classical optimization problem of minimizing a proper, convex and lower semicontinuous function via the...
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Accelerated gradient sliding for structured convex optimization
Our main goal in this paper is to show that one can skip gradient computations for gradient descent type methods applied to certain structured convex...
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On proper separation of convex sets
The aim of this contribution is to propose an alternative but equivalent statement of the proper separation of two closed convex sets in a...
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Linesearch Newton-CG methods for convex optimization with noise
This paper studies the numerical solution of strictly convex unconstrained optimization problems by linesearch Newton-CG methods. We focus on methods...
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Methodology and first-order algorithms for solving nonsmooth and non-strongly convex bilevel optimization problems
Simple bilevel problems are optimization problems in which we want to find an optimal solution to an inner problem that minimizes an outer objective...
