相关论文: Two Results on Slime Mold Computations

While the SLIM approach obtained high ranking-accuracy in many experiments in the literature, it is also known for its high computational cost of learning its parameters from data. For this reason, we focus in this paper on variants of…

Variational problems of splitting-type with mixed linear-superlinear growth conditions are considered. In the twodimensional case the minimizing problem is given by \[ J [w] = \int_{\Omega} \Big[f_1\big(\partial_1 w\big) +…

Discrete simulation methods are efficient tools to investigate the complex behaviors of complex fluids made of either dry granular materials or dilute suspensions. By contrast, materials made of soft and/or concentrated units (emulsions,…

With the approach of exascale computing era, particle-based models are becoming the focus of research due to their excellent scalability. We present a new code, Slurm, which implements the classic particle-in-cell algorithm for modeling…

We introduce a generalization of the linearized Alternating Direction Method of Multipliers to optimize a real-valued function $f$ of multiple arguments with potentially multiple constraints $g_\circ$ on each of them. The function $f$ may…

We suggest an adaptive version of a partial linearization method for composite optimization problems. The goal function is the sum of a smooth function and a non necessary smooth convex separable function, whereas the feasible set is the…

We design accelerated algorithms with improved rates for several fundamental classes of optimization problems. Our algorithms all build upon techniques related to the analysis of primal-dual extragradient methods via relative Lipschitzness…

We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be…

We consider minimizing an objective function subject to constraints defined by the intersection of lower-level sets of convex functions. We study two cases: (i) strongly convex and Lipschitz-smooth objective function and (ii) convex but…

In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on the knowledge of optimal…

In this paper, we combine the positive aspects of the Gradient Sampling (GS) and bundle methods, as the most efficient methods in nonsmooth optimization, to develop a robust method for solving unconstrained nonsmooth convex optimization…

The problem of optimizing over the cone of nonnegative polynomials is a fundamental problem in computational mathematics, with applications to polynomial optimization, control, machine learning, game theory, and combinatorics, among others.…

Globally non-positively curved, or CAT(0), polyhedral complexes arise in a number of applications, including evolutionary biology and robotics. These spaces have unique shortest paths and are composed of Euclidean polyhedra, yet many…

Multivariate polynomial optimization is a prevalent model for a number of engineering problems. From a mathematical viewpoint, polynomial optimization is challenging because it is non-convex. The Lasserre's theory, based on semidefinite…

Computing saddle points with a prescribed Morse index on potential energy surfaces is crucial for characterizing transition states for nosie-induced rare transition events in physics and chemistry. Many numerical algorithms for this type of…

The convergence behaviour of first-order methods can be severely slowed down when applied to high-dimensional non-convex functions due to the presence of saddle points. If, additionally, the saddles are surrounded by large plateaus, it is…

We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…

Results from molecular dynamics simulations of simple, structured particles capable of self-assembling into polyhedral shells are described. The analysis focuses on the growth histories of individual shells in the presence of an explicit…

Consider the problem of minimizing the sum of two convex functions, one being smooth and the other non-smooth. In this paper, we introduce a general class of approximate proximal splitting (APS) methods for solving such minimization…

A system consisting of a doubly clamped beam with an attached body (slider) free to move along the beam has been studied recently by multiple research groups. Under harmonic base excitation, the system has the capacity to passively adapt…