相关论文: An incremental descent method for multi-objective …

We present the Multilevel Bregman Proximal Gradient Descent (ML BPGD) method, a novel multilevel optimization framework tailored to constrained convex problems with relative Lipschitz smoothness. Our approach extends the classical…

In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for unconstrained MOPs by Fliege and Svaiter to constrained…

We prove that the finite-difference based derivative-free descent (FD-DFD) methods have a capability to find the global minima for a class of multiple minima problems. Our main result shows that, for a class of multiple minima objectives…

Multidimensional optimization problems where the objective function and the constraints are multiextremal non-differentiable Lipschitz functions (with unknown Lipschitz constants) and the feasible region is a finite collection of robust…

We consider the proximal-gradient method for minimizing an objective function that is the sum of a smooth function and a non-smooth convex function. A feature that distinguishes our work from most in the literature is that we assume that…

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…

Gradient methods are experiencing a growth in methodological and theoretical developments owing to the challenges posed by optimization problems arising in data science. However, such gradient methods face diverging optimality gaps or…

Gradient descent is a widely used iterative algorithm for finding local minima in multivariate functions. However, the final iterations often either overshoot the minima or make minimal progress, making it challenging to determine an…

In this paper, we deal with the Front Steepest Descent algorithm for multi-objective optimization. We point out that the algorithm from the literature is often incapable, by design, of spanning large portions of the Pareto front. We thus…

Stochastic multi-objective optimization (SMOO) has recently emerged as a powerful framework for addressing machine learning problems with multiple objectives. The bias introduced by the nonlinearity of the subproblem solution mapping…

Despite its important applications in Machine Learning, min-max optimization of nonconvex-nonconcave objectives remains elusive. Not only are there no known first-order methods converging even to approximate local min-max points, but the…

This paper proposes a new steepest gradient descent method for solving nonconvex finite minimax problems using non-monotone adaptive step sizes and providing proof of convergence results in cases of the nonconvex, quasiconvex, and…

The gradient descent method aims at finding local minima of a given multivariate function by moving along the direction of its gradient, and hence, the algorithm typically involves computing all partial derivatives of a given function,…

Universal methods for optimization are designed to achieve theoretically optimal convergence rates without any prior knowledge of the problem's regularity parameters or the accurarcy of the gradient oracle employed by the optimizer. In this…

We present an accelerated gradient method for non-convex optimization problems with Lipschitz continuous first and second derivatives. The method requires time $O(\epsilon^{-7/4} \log(1/ \epsilon) )$ to find an $\epsilon$-stationary point,…

Recommender systems need to mirror the complexity of the environment they are applied in. The more we know about what might benefit the user, the more objectives the recommender system has. In addition there may be multiple stakeholders -…

We propose a manifold AdaGrad-Norm method (\textsc{MAdaGrad}), which extends the norm version of AdaGrad (AdaGrad-Norm) to Riemannian optimization. In contrast to line-search schemes, which may require several exponential map computations…

Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…

Convergence of the gradient descent algorithm has been attracting renewed interest due to its utility in deep learning applications. Even as multiple variants of gradient descent were proposed, the assumption that the gradient of the…

Complex object wave recovery from single-shot interference pattern is an important practical problem in interferometry and digital holography. The most popular single-shot interferogram analysis method involves Fourier filtering of…