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By utilizing only depth information, the paper introduces a novel but efficient local planning approach that enhances not only computational efficiency but also planning performances for memoryless local planners. The sampling is first…
We propose a descent subgradient algorithm for unconstrained nonsmooth nonconvex multiobjective optimization problems. To find a descent direction, we present an iterative process that efficiently approximates the Goldstein subdifferential…
Feature transformation aims to generate new pattern-discriminative feature space from original features to improve downstream machine learning (ML) task performances. However, the discrete search space for the optimal feature explosively…
Approximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute…
In the present work, we introduce a Self-Consistent Density-Functional Embedding technique, which leaves the realm of standard energy-functional approaches in Density Functional Theory and targets directly the density-to-potential mapping…
We propose a new random method to minimize deterministic continuous functions over subsets $\mathcal{S}$ of high-dimensional space $\mathbb{R}^K$ without assuming convexity. Our procedure alternates between a Global Search (GS) regime to…
Novel coordinate descent (CD) methods are proposed for minimizing nonconvex functions consisting of three terms: (i) a continuously differentiable term, (ii) a simple convex term, and (iii) a concave and continuous term. First, by extending…
In this paper, a decentralized proximal method of multipliers (DPMM) is proposed to solve constrained convex optimization problems over multi-agent networks, where the local objective of each agent is a general closed convex function, and…
Many computer vision problems (e.g., camera calibration, image alignment, structure from motion) are solved with nonlinear optimization methods. It is generally accepted that second order descent methods are the most robust, fast, and…
The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…
This paper introduces a new deep learning approach to approximately solve the Covering Salesman Problem (CSP). In this approach, given the city locations of a CSP as input, a deep neural network model is designed to directly output the…
Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are…
We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…
Alternating Direction Method of Multipliers (ADMM) is a popular algorithm for distributed learning, where a network of nodes collaboratively solve a regularized empirical risk minimization by iterative local computation associated with…
Subgradient methods are the natural extension to the non-smooth case of the classical gradient descent for regular convex optimization problems. However, in general, they are characterized by slow convergence rates, and they require…
Dynamic spectrum management (DSM) has been recognized as a key technology to significantly improve the performance of digital subscriber line (DSL) broadband access networks. The basic concept of DSM is to coordinate transmission over…
This article is devoted to one particular case of using universal accelerated proximal envelopes to obtain computationally efficient accelerated versions of methods used to solve various optimization problem setups. In this paper, we…
This paper develops and analyzes an online distributed proximal-gradient method (DPGM) for time-varying composite convex optimization problems. Each node of the network features a local cost that includes a smooth strongly convex function…
Implicit regularization refers to the tendency of local search algorithms to converge to low-dimensional solutions, even when such structures are not explicitly enforced. Despite its ubiquity, the mechanism underlying this behavior remains…
We propose a trust-region method for finite-sum minimization with an adaptive sample size adjustment technique, which is practical in the sense that it leads to a globally convergent method that shows strong performance empirically without…