Related papers: Three-point Step Size Gradient Method with Relaxed…
In this paper we propose a corrected semi-proximal ADMM (alternating direction method of multipliers) for the general $p$-block $(p\!\ge 3)$ convex optimization problems with linear constraints, aiming to resolve the dilemma that almost all…
This paper considers the online scenario using the Barzilai-Borwein Quasi-Newton Method. In an online optimization problem, an online agent uses a certain algorithm to decide on an objective at each time step after which a possible loss is…
In this paper, we are interested in finding the global minimizer of a nonsmooth nonconvex unconstrained optimization problem. By combining the discrete consensus-based optimization (CBO) algorithm and the gradient descent method, we develop…
In this paper, we propose a quasi Newton method to solve the robust counterpart of an uncertain multiobjective optimization problem under an arbitrary finite uncertainty set. Here the robust counterpart of an uncertain multiobjective…
In this work, we develop new optimization algorithms that use approximate second-order information combined with the gradient regularization technique to achieve fast global convergence rates for both convex and non-convex objectives. The…
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…
We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly non differentiable, function. The key features of the proposed method are the definition of a…
We present a stochastic inexact Gauss-Newton method for the solution of nonlinear least-squares. To reduce the computational cost with respect to the classical method, at each iteration the proposed algorithm approximately minimizes the…
We consider the composite minimization problem with the objective function being the sum of a continuously differentiable and a merely lower semicontinuous and extended-valued function. The proximal gradient method is probably the most…
Optimization problems with composite functions consist of an objective function which is the sum of a smooth and a (convex) nonsmooth term. This particular structure is exploited by the class of proximal gradient methods and some of their…
In this paper, we consider the unconstrained multiobjective optimization problem. In recent years, researchers pointed out that the steepest decent method may generate small stepsize which leads to slow convergence rates. To address the…
This paper considers a networked system with a finite number of users and supposes that each user tries to minimize its own private objective function over its own private constraint set. It is assumed that each user's constraint set can be…
The proximal gradient algorithm for minimizing the sum of a smooth and a nonsmooth convex function often converges linearly even without strong convexity. One common reason is that a multiple of the step length at each iteration may…
In this paper, we propose a new non-monotone line-search method for smooth unconstrained optimization problems with objective functions that have many non-global local minimizers. The method is based on a relaxed Armijo condition that…
A wider selection of step sizes is explored for the distributed subgradient algorithm for multi-agent optimization problems, for both time-invariant and time-varying communication topologies. The square summable requirement of the step…
We suggest simple modifications of the conditional gradient method for smooth optimization problems, which maintain the basic convergence properties, but reduce the implementation cost of each iteration essentially. Namely, we propose the…
This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic…
The choice of the stepsize in first-order convex optimization is typically based on the smoothness constant and plays a crucial role in the performance of algorithms. Recently, there has been a resurgent interest in introducing adaptive…
One of the major issues in stochastic gradient descent (SGD) methods is how to choose an appropriate step size while running the algorithm. Since the traditional line search technique does not apply for stochastic optimization algorithms,…
We consider a distributed multi-agent optimization problem over a time-invariant undirected graph, where each agent possesses a local objective function and all agents collaboratively minimize the average of all objective functions through…