Related papers: Near-Optimal Convex Simple Bilevel Optimization wi…

In this work, we develop analysis and algorithms for a class of (stochastic) bilevel optimization problems whose lower-level (LL) problem is strongly convex and linearly constrained. Most existing approaches for solving such problems rely…

Recently some specific classes of non-smooth and non-Lipschitz convex optimization problems were selected by Yu.~Nesterov along with H.~Lu. We consider convex programming problems with similar smoothness conditions for the objective…

A framework is presented whereby a general convex conic optimization problem is transformed into an equivalent convex optimization problem whose only constraints are linear equations and whose objective function is Lipschitz continuous.…

For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…

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…

This paper studies a multiobjective bilevel optimization problem where each objective is a fractional function. By reformulating the problem into a single-level one, we establish refined necessary and sufficient optimality conditions. These…

The convergence behavior of gradient methods for minimizing convex differentiable functions is one of the core questions in convex optimization. This paper shows that their well-known complexities can be achieved under conditions weaker…

Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…

We consider bilevel optimization problems with general nonconvex lower-level objectives and show that the classical hyperfunction-based formulation is unsettled, since the global minimizer of the lower-level problem is generally…

We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…

We study the complexity of optimizing highly smooth convex functions. For a positive integer $p$, we want to find an $\epsilon$-approximate minimum of a convex function $f$, given oracle access to the function and its first $p$ derivatives,…

A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…

Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…

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…

When minimizing a multiobjective optimization problem (MOP) using multiobjective gradient descent methods, the imbalances among objective functions often decelerate the convergence. In response to this challenge, we propose two types of the…

Two-level stochastic optimization formulations have become instrumental in a number of machine learning contexts such as continual learning, neural architecture search, adversarial learning, and hyperparameter tuning. Practical stochastic…

In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…

Bilevel optimization recently has attracted increased interest in machine learning due to its many applications such as hyper-parameter optimization and meta learning. Although many bilevel methods recently have been proposed, these methods…

Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…

We propose efficient methods for solving stochastic simple bilevel optimization problems with convex inner levels, where the goal is to minimize an outer stochastic objective function subject to the solution set of an inner stochastic…