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The Quantum Approximate Optimization Algorithm (QAOA) adopts a hybrid quantum-classical approach to find approximate solutions to variational optimization problems. In fact, it relies on a classical subroutine to optimize the parameters of…

Identifying active constraints from a point near an optimal solution is important both theoretically and practically in constrained continuous optimization, as it can help identify optimal Lagrange multipliers and essentially reduces an…

Using quasi-Newton methods in stochastic optimization is not a trivial task given the difficulty of extracting curvature information from the noisy gradients. Moreover, pre-conditioning noisy gradient observations tend to amplify the noise.…

Bayesian optimization devolves the global optimization of a costly objective function to the global optimization of a sequence of acquisition functions. This inner-loop optimization can be catastrophically difficult if it involves posterior…

Variable selection in linear regression has been a central topic in statistical research for decades. Bayesian variable selection methods, which account for uncertainty in both the regression coefficients and the noise variance, have…

We develop a mesh-free, derivative-free, matrix-free, and highly parallel localized stochastic method for high-dimensional semilinear parabolic PDEs. The efficiency of the proposed method is built upon four essential components: (i) a…

Multi-objective Bayesian optimization (MOBO) struggles with sparse (non-space-filling), scarce (limited observations) datasets affected by experimental uncertainty, where identical inputs can yield varying outputs. These challenges are…

Learning with label dependent label noise has been extensively explored in both theory and practice; however, dealing with instance (i.e., feature) and label dependent label noise continues to be a challenging task. The difficulty arises…

Many expensive black-box optimisation problems are sensitive to their inputs. In these problems it makes more sense to locate a region of good designs, than a single-possibly fragile-optimal design. Expensive black-box functions can be…

The flexible job shop scheduling problem with sequencing flexibility and position-based learning effect is considered in the present work. In [K. A. G. Araujo, E. G. Birgin, and D. P. Ronconi, Technical Report MCDO02022024, 2024], models,…

This paper studies worst-case robust optimal tracking using noisy input-output data. We utilize behavioral system theory to represent system trajectories, while avoiding explicit system identification. We assume that the recent output data…

Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…

In this paper, we focus on finding the global minimizer of a general unconstrained nonsmooth nonconvex optimization problem. Taking advantage of the smoothing method and the consensus-based optimization (CBO) method, we propose a novel…

Many state estimation algorithms must be tuned given the state space process and observation models, the process and observation noise parameters must be chosen. Conventional tuning approaches rely on heuristic hand-tuning or gradient-based…

In this work we develop a discretisation method for the Brinkman problem that is uniformly well-behaved in all regimes (as identified by a local dimensionless number with the meaning of a friction coefficient) and supports general meshes as…

In this paper, we present an open-source pure-Python library called PyPop7 for black-box optimization (BBO). As population-based methods (e.g., evolutionary algorithms, swarm intelligence, and pattern search) become increasingly popular for…

Gradient-based solvers risk convergence to local optima, leading to incorrect researcher inference. Heuristic-based algorithms are able to ``break free" of these local optima to eventually converge to the true global optimum. However, given…

This paper studies Byzantine-robust stochastic optimization over a decentralized network, where every agent periodically communicates with its neighbors to exchange local models, and then updates its own local model by stochastic gradient…

This paper considers the efficient minimization of the infinite time average of a stationary ergodic process in the space of a handful of design parameters which affect it. Problems of this class, derived from physical or numerical…

In this work we consider unconstrained optimization problems. The objective function is known through a zeroth order stochastic oracle that gives an estimate of the true objective function. To solve these problems, we propose a…