Related papers: On the implementation of a global optimization met…
In this paper, we develop a global descent method for non-convex multi-objective optimization problems. The proposed approach builds upon foundational concepts from single-objective global descent techniques while removing the need for…
This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…
Gaussian process (GP) models are commonly used statistical metamodels for emulating expensive computer simulators. Fitting a GP model can be numerically unstable if any pair of design points in the input space are close together. Ranjan,…
Increasing the degrees of freedom of robotic systems makes them more versatile and flexible. This usually renders the system kinematically redundant: the main manipulation or interaction task does not fully determine its joint maneuvers.…
Solving partial differential equations (PDEs) on manifolds defined by randomly sampled point clouds is a challenging problem in scientific computing and has broad applications in various fields. In this paper, we develop a two-step…
Gravitational field modelling is an important tool for inferring past and present dynamic processes of the Earth. Functions on the sphere such as the gravitational potential are usually expanded in terms of either spherical harmonics or…
Mixed-integer programming (MIP) has emerged as a powerful framework for learning optimal decision trees. Yet, existing MIP approaches for regression tasks are either limited to purely binary features or become computationally intractable…
In a recent work, we presented the reduced Jacobian method (RJM) as an extension of Wolfe's reduced gradient method to multicriteria (multiobjective) optimization problems dealing with linear constraints. This approach reveals that using a…
This paper introduces unified projection-free Frank-Wolfe type algorithms for adversarial continuous DR-submodular optimization, spanning scenarios such as full information and (semi-)bandit feedback, monotone and non-monotone functions,…
Bilevel Optimization has experienced significant advancements recently with the introduction of new efficient algorithms. Mirroring the success in single-level optimization, stochastic gradient-based algorithms are widely used in bilevel…
In this paper we extend the core branch-and-bound algorithm of an RLT-based solver for continuous polynomial optimization, RAPOSa, to handle mixed-integer problems. We do so by a direct adaptation, in which LP relaxations are replaced with…
In the paper, we generalize the approach Gasnikov et. al, 2017, which allows to solve (stochastic) convex optimization problems with an inexact gradient-free oracle, to the convex-concave saddle-point problem. The proposed approach works,…
We propose UPOQA, a derivative-free optimization algorithm for partially separable unconstrained problems, leveraging quadratic interpolation and a structured trust-region framework. By decomposing the objective into element functions,…
We develop new algorithms for Riemannian bilevel optimization. We focus in particular on batch and stochastic gradient-based methods, with the explicit goal of avoiding second-order information such as Riemannian hyper-gradients. We propose…
We present a method to solve two-stage stochastic problems with fixed recourse when the uncertainty space can have either discrete or continuous distributions. Given a partition of the uncertainty space, the method is addressed to solve a…
In this paper, we study the following robust optimization problem. Given an independence system and candidate objective functions, we choose an independent set, and then an adversary chooses one objective function, knowing our choice. Our…
Many real world applications can be framed as multi-objective optimization problems, where we wish to simultaneously optimize for multiple criteria. Bayesian optimization techniques for the multi-objective setting are pertinent when the…
In this paper, a new sequential surrogate-based optimization (SSBO) algorithm is developed, which aims to improve the global search ability and local search efficiency for the global optimization of expensive black-box models. The proposed…
This paper introduces a novel meshfree methodology based on Radial Basis Function-Finite Difference (RBF-FD) approximations for the numerical solution of partial differential equations (PDEs) on surfaces of codimension 1 embedded in…
Conjugate gradient (CG) methods are widely acknowledged as efficient for minimizing continuously differentiable functions in Euclidean spaces. In recent years, various CG methods have been extended to Riemannian manifold optimization, but…