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We introduce new global and local inexact oracle concepts for a wide class of convex functions in composite convex minimization. Such inexact oracles naturally come from primal-dual framework, barrier smoothing, inexact computations of…
The global optimization literature places large emphasis on reducing intractable optimization problems into more tractable structured optimization forms. In order to achieve this goal, many existing methods are restricted to optimization…
We study Consensus-Based Optimization (CBO) for two-layer neural network training. We compare the performance of CBO against Adam on two test cases and demonstrate how a hybrid approach, combining CBO with Adam, provides faster convergence…
Techniques involving factorization are found in a wide range of applications and have enjoyed significant empirical success in many fields. However, common to a vast majority of these problems is the significant disadvantage that the…
In constrained Markov decision processes, enforcing constraints during training is often thought of as decreasing the final return. Recently, it was shown that constraints can be incorporated directly into the policy geometry, yielding an…
This note describes a parameter-free implementation of Central Force Optimization for deterministic multidimensional search and optimization. The user supplies only one input: the objective function to be maximized, nothing more. The CFO…
Newton-type methods enjoy fast local convergence and strong empirical performance, but achieving global guarantees comparable to first-order methods remains challenging. Even for simple strongly convex problems, no straightforward variant…
Motivated by economic dispatch and linearly-constrained resource allocation problems, this paper proposes a class of novel Distributed-Approx Newton algorithms that approximate the standard Newton optimization method. We first develop the…
Motivated by applications in production planning and storage allocation in hierarchical databases, we initiate the study of covering partially ordered items (CPO). Given a capacity $k \in \mathbb{Z}^+$, and a directed graph $G=(V,E)$ where…
Data-driven algorithms, in particular neural networks, can emulate the effect of sub-grid scale processes in coarse-resolution climate models if trained on high-resolution climate simulations. However, they may violate key physical…
Given a parametrized family of finite frames, we consider the optimization problem of finding the member of this family whose coefficient space most closely contains a given data vector. This nonlinear least squares problem arises naturally…
Local tensor methods are a class of optimization algorithms that was introduced in [Hastings,arXiv:1905.07047v2][1] as a classical analogue of the quantum approximate optimization algorithm (QAOA). These algorithms treat the cost function…
Limited resources motivate decomposing large-scale problems into smaller,``local" subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of ``local hardness", i.e.,…
We introduce a new class of objectives for optimal transport computations of datasets in high-dimensional Euclidean spaces. The new objectives are parametrized by $\rho \geq 1$, and provide a metric space $\mathcal{R}_{\rho}(\cdot, \cdot)$…
Purpose: Optimization challenges in science, engineering, and real-world applications often involve complex, high-dimensional, and multimodal search spaces. Traditional optimization methods frequently struggle with local optima entrapment,…
This paper is concerned with numerically finding a global solution of constrained optimal control problems with many local minima. The focus is on the optimal decentralized control (ODC) problem, whose feasible set is recently shown to have…
We propose a unified derivative-free proximal Newton-type algorithm framework for solving composite optimization problems formulated as the sum of a black-box function and a known regularization term. We establish the iteration and oracle…
Global optimisation problems in high-dimensional and infinite dimensional spaces arise in various real-world applications such as engineering, economics, geophysics, biology, machine learning, optimal control, etc. Among stochastic…
In machine learning, nonconvex optimization problems with multiple local optimums are often encountered. Graduated Optimization Algorithm (GOA) is a popular heuristic method to obtain global optimums of nonconvex problems through…
Hidden convex optimization is such a class of nonconvex optimization problems that can be globally solved in polynomial time via equivalent convex programming reformulations. In this paper, we focus on checking local optimality in hidden…