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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...
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Convergence of a Weighted Barrier Algorithm for Stochastic Convex Quadratic Semidefinite Optimization
Mehrotra and Özevin (SIAM J Optim 19:1846–1880, 2009) computationally found that a weighted barrier decomposition algorithm for two-stage stochastic...
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Exterior-Point Optimization for Sparse and Low-Rank Optimization
Many problems of substantial current interest in machine learning, statistics, and data science can be formulated as sparse and low-rank optimization...
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A Multi-Scale Method for Distributed Convex Optimization with Constraints
This paper proposes a multi-scale method to design a continuous-time distributed algorithm for constrained convex optimization problems by using...
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A Stochastic Nesterov’s Smoothing Accelerated Method for General Nonsmooth Constrained Stochastic Composite Convex Optimization
We propose a novel stochastic Nesterov’s smoothing accelerated method for general nonsmooth, constrained, stochastic composite convex optimization,...
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Relationships Between Polyhedral Convex Sets and Generalized Polyhedral Convex Sets
In this paper, we study some relationships between polyhedral convex sets and generalized polyhedral convex sets. In particular, we clarify by a...
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A generalized Frank–Wolfe method with “dual averaging” for strongly convex composite optimization
We propose a simple variant of the generalized Frank–Wolfe method for solving strongly convex composite optimization problems, by introducing an...
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Convex generalized Nash equilibrium problems and polynomial optimization
This paper studies convex generalized Nash equilibrium problems that are given by polynomials. We use rational and parametric expressions for...
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Step-Affine Functions, Halfspaces, and Separation of Convex Sets with Applications to Convex Optimization Problems
We introduce the class of step-affine functions defined on a real vector space and establish the duality between step-affine functions and...
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Convex optimization via inertial algorithms with vanishing Tikhonov regularization: fast convergence to the minimum norm solution
In a Hilbertian framework, for the minimization of a general convex differentiable function f , we introduce new inertial dynamics and algorithms that...
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Gradient-free Federated Learning Methods with l1 and l2-randomization for Non-smooth Convex Stochastic Optimization Problems
AbstractThis paper studies non-smooth problems of convex stochastic optimization. Using the smoothing technique based on the replacement of the...
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A piecewise conservative method for unconstrained convex optimization
We consider a continuous-time optimization method based on a dynamical system, where a massive particle starting at rest moves in the conservative...
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Block preconditioners for linear systems in interior point methods for convex constrained optimization
In this paper, we address the preconditioned iterative solution of the saddle-point linear systems arising from the (regularized) Interior Point...
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Convergence rates for the heavy-ball continuous dynamics for non-convex optimization, under Polyak–Łojasiewicz condition
We study convergence of the trajectories of the Heavy Ball dynamical system, with constant dam** coefficient, in the framework of convex and...
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Stochastic first-order methods for convex and nonconvex functional constrained optimization
Functional constrained optimization is becoming more and more important in machine learning and operations research. Such problems have potential...
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An Easy Path to Convex Analysis and Applications
This book examines the most fundamental parts of convex analysis and its applications to optimization and location problems. Accessible techniques of...
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Almost sure convergence of stochastic composite objective mirror descent for non-convex non-smooth optimization
Stochastic composite objective mirror descent (SCOMID) is an effective method for solving large-scale stochastic composite problems in machine...
