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We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…
Combinatorial optimization (CO) problems arise across a broad spectrum of domains, including medicine, logistics, and manufacturing. While exact solutions are often computationally infeasible, many practical applications require…
This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…
Optimising discrete data for a desired characteristic using gradient-based methods involves projecting the data into a continuous latent space and carrying out optimisation in this space. Carrying out global optimisation is difficult as…
Gradient-based methods are widely used to solve various optimization problems, however, they are either constrained by local optima dilemmas, simple convex constraints, and continuous differentiability requirements, or limited to…
We present a gradient-based optimal-control technique for open quantum systems that utilizes quantum trajectories to simulate the quantum dynamics during optimization. Using trajectories allows for optimizing open systems with less…
In this paper, we present the Monte-Carlo Compressive Optimization algorithm, a new method to solve a combinatorial optimization problem that is assumed compressible. The method relies on random queries to the objective function in order to…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…
We analyze an optimization problem of the conductivity in a composite material arising in a heat conduction energy storage problem. The model is described by the heat equation that specifies the heat exchange between two types of materials…
The replica-exchange Monte-Carlo (RXMC) method is a powerful Markov-chain Monte-Carlo algorithm for sampling from multi-modal distributions, which are challenging for conventional methods. The sampling efficiency of the RXMC method depends…
In a Hilbert setting, for convex differentiable optimization, we develop a general framework for adaptive accelerated gradient methods. They are based on damped inertial dynamics where the coefficients are designed in a closed-loop way.…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
Gradient-based optimization methods are commonly used to identify local optima in high-dimensional spaces. When derivatives cannot be evaluated directly, stochastic estimators can provide approximate gradients. However, these estimators'…
A broad class of hybrid quantum-classical algorithms known as "variational algorithms" have been proposed in the context of quantum simulation, machine learning, and combinatorial optimization as a means of potentially achieving a quantum…
We develop an optimization-based approach to the problem of reconstructing temperature-dependent material properties in complex thermo-fluid systems described by the equations for the conservation of mass, momentum and energy. Our goal is…
The conjugate gradient method is a widely used algorithm for the numerical solution of a system of linear equations. It is particularly attractive because it allows one to take advantage of sparse matrices and produces (in case of infinite…
We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
While gradient-based discrete samplers are effective in sampling from complex distributions, they are susceptible to getting trapped in local minima, particularly in high-dimensional, multimodal discrete distributions, owing to the…
In this paper, acceleration of gradient methods for convex optimization problems with weak levels of convexity and smoothness is considered. Starting from the universal fast gradient method which was designed to be an optimal method for…