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Branch-and-Bound (B&B) algorithms are time intensive tree-based exploration methods for solving to optimality combinatorial optimization problems. In this paper, we investigate the use of GPU computing as a major complementary way to speed…
We present gPC-SCP: Generalized Polynomial Chaos-based Sequential Convex Programming to compute a sub-optimal solution for a continuous-time chance-constrained stochastic nonlinear optimal control (SNOC) problem. The approach enables motion…
In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…
The method of harmonic balance (HB) is a spectrally accurate method used to obtain periodic steady state solutions to dynamical systems subjected to periodic perturbations. We adapt HB to solve for the stress response of the Giesekus model…
Spatial Branch and Bound (B&B) algorithms are widely used for solving nonconvex problems to global optimality, yet they remain computationally expensive. Though some works have been carried out to speed up B&B via CPU parallelization, GPU…
We develop a method for the evaluation of extreme event statistics associated with nonlinear dynamical systems, using a small number of samples. From an initial dataset of design points, we formulate a sequential strategy that provides the…
Several combinatorial optimization problems can be solved with NISQ devices once that a corresponding quadratic unconstrained binary optimization (QUBO) form is derived. The aim of this work is to drastically reduce the variables needed for…
The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled…
Solving systems of Boolean equations is a fundamental task in symbolic computation and algebraic cryptanalysis, with wide-ranging applications in cryptography, coding theory, and formal verification. Among existing approaches, the Boolean…
Although many real-world stochastic planning problems are more naturally formulated by hybrid models with both discrete and continuous variables, current state-of-the-art methods cannot adequately address these problems. We present the…
This work addresses the uniform parallel machine scheduling problem within an optimistic bilevel optimization framework. The leader seeks to minimize the weighted number of tardy jobs, while the follower aims to minimize the total…
Continuous search problems (CSPs), which involve finding solutions within a continuous domain, frequently arise in fields such as optimization, physics, and engineering. Unlike discrete search problems, CSPs require navigating an…
Many systems exhibit a mixture of continuous and discrete dynamics. We consider a family of mixed-integer non-convex non-linear optimisation problems obtained in discretisations of optimal control of such systems. For this family, a…
This paper considers distributed optimization algorithms, with application in binary classification via distributed support-vector-machines (D-SVM) over multi-agent networks subject to some link nonlinearities. The agents solve a…
Curvilinear, multiblock summation-by-parts finite difference operators with the simultaneous approximation term method provide a stable and accurate framework for solving the wave equation in second order form. That said, the standard…
In this paper, we consider an approach to the parallelizing of the algorithms realizing the modified probability changigng method with adaptation and partial rollback procedure for constrained pseudo-Boolean optimization problems. Existing…
We develop a tractable and flexible approach for incorporating side information into dynamic optimization under uncertainty. The proposed framework uses predictive machine learning methods (such as $k$-nearest neighbors, kernel regression,…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
Hard optimization problems are often approached by finding approximate solutions. Here, we highlight the concept of proportional sampling and discuss how it can be used to improve the performance of stochastic algorithms for optimization.…
In this paper, we evaluate stochastic-computing simulated annealing (SC-SA) for solving large-scale combinatorial optimization problems. SC-SA is designed using stochastic computing, where the computatoin is reazlied using random bitstream,…