相关论文: ItsDEAL: Inexact two-level smoothing descent algor…

In this paper, we study inexact high-order Tensor Methods for solving convex optimization problems with composite objective. At every step of such methods, we use approximate solution of the auxiliary problem, defined by the bound for the…

This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…

In order to solve the minimization of a nonsmooth convex function, we design an inertial second-order dynamic algorithm, which is obtained by approximating the nonsmooth function by a class of smooth functions. By studying the asymptotic…

Inverse problem or parameter estimation of ordinary differential equations (ODEs), the iterative process of minimizing the mismatch between model-predicted and experimental states by tuning the parameter values within an optimization…

This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…

Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…

In this paper we propose accelerated gradient descent schemes for convex optimization problems in Hilbert space. We consider inexact oracle case.

In this paper, we have studied a decomposition method for solving a class of nonconvex two-stage stochastic programs, where both the objective and constraints of the second-stage problem are nonlinearly parameterized by the first-stage…

In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem.…

Incremental methods are widely utilized for solving finite-sum optimization problems in machine learning and signal processing. In this paper, we study a family of incremental methods -- including incremental subgradient, incremental…

Many real-world problems not only have complicated nonconvex functional constraints but also use a large number of data points. This motivates the design of efficient stochastic methods on finite-sum or expectation constrained problems. In…

In this paper, we focus on simple bilevel optimization problems, where we minimize a convex smooth objective function over the optimal solution set of another convex smooth constrained optimization problem. We present a novel bilevel…

In this paper we consider stochastic weakly convex composite problems, however without the existence of a stochastic subgradient oracle. We present a derivative free algorithm that uses a two point approximation for computing a gradient…

In this paper, we propose a new method based on the Sliding Algorithm from Lan(2016, 2019) for the convex composite optimization problem that includes two terms: smooth one and non-smooth one. Our method uses the stochastic noised…

This paper derives a discrete dual problem for a prototypical hybrid high-order method for convex minimization problems. The discrete primal and dual problem satisfy a weak convex duality that leads to a priori error estimates with…

In this work, we study nonconvex-strongly convex online bilevel optimization (OBO) using only first-order oracle. Existing OBO algorithms are mainly based on hypergradient descent, which requires access to a Hessian-vector product (HVP)…

In this paper, we consider Frank-Wolfe-based algorithms for composite convex optimization problems with objective involving a logarithmically-homogeneous, self-concordant functions. Recent Frank-Wolfe-based methods for this class of…

Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…

Bilevel programming has recently received a great deal of attention due to its abundant applications in many areas. The optimal value function approach provides a useful reformulation of the bilevel problem, but its utility is often limited…

Recent advances (Sherman, 2017; Sidford and Tian, 2018; Cohen et al., 2021) have overcome the fundamental barrier of dimension dependence in the iteration complexity of solving $\ell_\infty$ regression with first-order methods. Yet it…