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Oscillator Ising machines (OIMs) are networks of coupled oscillators that seek the minimum energy state of an Ising model. Since many NP-hard problems are equivalent to the minimization of an Ising Hamiltonian, OIMs have emerged as a…
Bayesian optimization (BO) is a popular global optimization scheme for sample-efficient optimization in domains with expensive function evaluations. The existing BO techniques are capable of finding a single global optimum solution.…
Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…
We consider the global minimization of a particular type of minimum structured optimization problems wherein the variables must belong to some basic set, the feasible domain is described by the intersection of a large number of functional…
We analyze Newton's method with lazy Hessian updates for solving general possibly non-convex optimization problems. We propose to reuse a previously seen Hessian for several iterations while computing new gradients at each step of the…
Purpose: To describe and mathematically validate the superiorization methodology, which is a recently-developed heuristic approach to optimization, and to discuss its applicability to medical physics problem formulations that specify the…
Bayesian optimization (BO) has gained attention as an efficient algorithm for black-box optimization of expensive-to-evaluate systems, where the BO algorithm iteratively queries the system and suggests new trials based on a probabilistic…
In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature range around the critical point. By combining the parallel tempering algorithm with cluster updates and an…
Global polynomial optimization is an important tool across applied mathematics, with many applications in operations research, engineering, and physical sciences. In various settings, the polynomials depend on external parameters that may…
Mathematical solvers use parametrized Optimization Problems (OPs) as inputs to yield optimal decisions. In many real-world settings, some of these parameters are unknown or uncertain. Recent research focuses on predicting the value of these…
Binary optimisation tasks are ubiquitous in areas ranging from logistics to cryptography. The exponential complexity of such problems means that the performance of traditional computational methods decreases rapidly with increasing problem…
The goal of this paper is to solve a class of high-order polynomial benchmark optimization problems, including the Goldstein-Price problem and the Three Hump Camel Back problem. By using a generalized canonical duality theory, we are able…
Bayesian optimization is normally performed within fixed variable bounds. In cases like hyperparameter tuning for machine learning algorithms, setting the variable bounds is not trivial. It is hard to guarantee that any fixed bounds will…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
In this paper, we provide a mathematical framework for improving generalization in a class of learning problems which is related to point estimations for modeling of high-dimensional nonlinear functions. In particular, we consider a…
Existing value function approximation methods have been successfully used in many applications, but they often lack useful a priori error bounds. We propose a new approximate bilinear programming formulation of value function approximation,…
We provide several quantum algorithms for continuous optimization that do not require gradient estimation. Instead, we encode the optimization problem into the dynamics of a physical system and coherently simulate the time evolution. We…
In this paper, we propose a globally convergent Newton type method to solve $\ell_0$ regularized sparse optimization problem. In fact, a line search strategy is applied to the Newton method to obtain global convergence. The Jacobian matrix…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…
Krentel [J. Comput. System. Sci., 36, pp.490--509] presented a framework for an NP optimization problem that searches an optimal value among exponentially-many outcomes of polynomial-time computations. This paper expands his framework to a…