Related papers: Nonlinear Conjugate Gradient Method for Multiobjec…
Backtracking line-search is an old yet powerful strategy for finding a better step sizes to be used in proximal gradient algorithms. The main principle is to locally find a simple convex upper bound of the objective function, which in turn…
This paper considers non-smooth optimization problems where we seek to minimize the pointwise maximum of a continuously parameterized family of functions. Since the objective function is given as the solution to a maximization problem,…
Conditional gradient algorithms (also often called Frank-Wolfe algorithms) are popular due to their simplicity of only requiring a linear optimization oracle and more recently they also gained significant traction for online learning. While…
The canonical solution methodology for finite constrained Markov decision processes (CMDPs), where the objective is to maximize the expected infinite-horizon discounted rewards subject to the expected infinite-horizon discounted costs…
The linear conjugate gradient method is an efficient iterative method for the convex quadratic minimization problems $ \mathop {\min }\limits_{x \in { \mathbb R^n}} f(x) =\dfrac{1}{2}x^TAx+b^Tx $, where $ A \in R^{n \times n} $ is symmetric…
We study numerical methods for the solution of general linear moment problems, where the solution belongs to a family of nested subspaces of a Hilbert space. Multi-level algorithms, based on the conjugate gradient method and the…
We consider nonsmooth optimization problems under affine constraints, where the objective consists of the average of the component functions of a large number $N$ of agents, and we only assume access to the Fenchel conjugate of the…
This paper treats the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We present and analyze several different optimality criteria which are based on the notions of stationarity and…
The co-localization problem is a model that simultaneously localizes objects of the same class within a series of images or videos. In \cite{joulin2014efficient}, authors present new variants of the Frank-Wolfe algorithm (aka conditional…
We investigate a class of nonconvex optimization problems characterized by a feasible set consisting of level-bounded nonconvex regularizers, with a continuously differentiable objective. We propose a novel hybrid approach to tackle such…
This paper focuses on the decentralized optimization (minimization and saddle point) problems with objective functions that satisfy Polyak-{\L}ojasiewicz condition (PL-condition). The first part of the paper is devoted to the minimization…
This paper proposes an extra gradient Anderson-accelerated algorithm for solving pseudomonotone variational inequalities, which uses the extra gradient scheme with line search to guarantee the global convergence and Anderson acceleration to…
Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the strong convexity parameter remains a challenge; moreover, even…
As the interest in multi- and many-objective optimization algorithms grows, the performance comparison of these algorithms becomes increasingly important. A large number of performance indicators for multi-objective optimization algorithms…
We describe a novel algorithm for solving general parametric (nonlinear) eigenvalue problems. Our method has two steps: first, high-accuracy solutions of non-parametric versions of the problem are gathered at some values of the parameters;…
Classification, recommendation, and ranking problems often involve competing goals with additional constraints (e.g., to satisfy fairness or diversity criteria). Such optimization problems are quite challenging, often involving non-convex…
This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework formulates these problems as network models, in that enumerating the Pareto frontier…
High dimensional and/or nonconvex optimization remains a challenging and important problem across a wide range of fields, such as machine learning, data assimilation, and partial differential equation (PDE) constrained optimization. Here we…
This paper introduces a graph-based algorithm for solving single-item, single-location inventory lot-sizing problems under non-stationary stochastic demand using the $(R_t, S_t)$ policy and a penalty cost scheme. The proposed method relaxes…
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…