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In this paper, we investigate a class of constrained saddle point (SP) problems where the objective function is nonconvex-concave and smooth. This class of problems has wide applicability in machine learning, including robust multi-class…
Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…
In this work we consider an iterative method for solving the quasi-convex feasibility problem. We firstly introduce the so-called star subgradient projection operator and present some useful properties. We subsequently obtain a convergence…
This paper develops two parameter-free methods for solving convex and strongly convex hybrid composite optimization problems, namely, a composite subgradient type method and a proximal bundle type method. Functional complexity bounds for…
An adaptive proximal method for a special class of variational inequalities and related problems is proposed. For example, the so-called mixed variational inequalities and composite saddle problems are considered. Some estimates of the…
We present a novel class of projected gradient (PG) methods for minimizing a smooth but not necessarily convex function over a convex compact set. We first provide a novel analysis of the constant-stepsize PG method, achieving the…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
Projected gradient methods are widely used for constrained optimization. A key application is for partial differential equations (PDEs), where the objective functional represents physical energy and the linear constraints enforce…
We investigate the method of conjugate gradients, exploiting inaccurate matrix-vector products, for the solution of convex quadratic optimization problems. Theoretical performance bounds are derived, and the necessary quantities occurring…
The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved nonconvex…
This paper focuses on developing a conditional gradient algorithm for multiobjective optimization problems with an unbounded feasible region. We employ the concept of recession cone to establish the well-defined nature of the algorithm. The…
We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines smoothing and homotopy techniques under the CGM framework, and provably achieves the optimal…
The implicit convex feasibility problem attempts to find a point in the intersection of a finite family of convex sets, some of which are not explicitly determined but may vary. We develop simultaneous and sequential projection methods…
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…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
In this work, based on the continuous time approach, we propose an accelerated gradient method with adaptive residual restart for convex multiobjective optimization problems. For the first, we derive rigorously the continuous limit of the…
This paper studies the primal-dual convergence and iteration-complexity of proximal bundle methods for solving nonsmooth problems with convex structures. More specifically, we develop a family of primal-dual proximal bundle methods for…
We analyse the behaviour of the newly introduced cyclic Douglas-Rachford algorithm for finding a point in the intersection of a finite number of closed convex sets. This work considers the case in which the target intersection set is…
In this paper, we propose and analyze an inexact version of the symmetric proximal alternating direction method of multipliers (ADMM) for solving linearly constrained optimization problems. Basically, the method allows its first subproblem…
In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility…