Related papers: Sampling-Based Global Optimal Control and Estimati…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
As we know, some global optimization problems cannot be solved using analytic methods, so numeric/algorithmic approaches are used to find near to the optimal solutions for them. A stochastic global optimization algorithm (SGoal) is an…
We study planted problems---finding hidden structures in random noisy inputs---through the lens of the sum-of-squares semidefinite programming hierarchy (SoS). This family of powerful semidefinite programs has recently yielded many new…
This work proposes a new moment-SOS hierarchy, called CS-TSSOS, for solving large-scale sparse polynomial optimization problems. Its novelty is to exploit simultaneously correlative sparsity and term sparsity by combining advantages of two…
This paper describes a data-driven framework for approximate global optimization in which precomputed solutions to a sample of problems are retrieved and adapted during online use to solve novel problems. This approach has promise for…
Quantum machine learning with quantum kernels for classification problems is a growing area of research. Recently, quantum kernel alignment techniques that parameterise the kernel have been developed, allowing the kernel to be trained and…
As the size and richness of available datasets grow larger, the opportunities for solving increasingly challenging problems with algorithms learning directly from data grow at the same pace. Consequently, the capability of learning…
This work investigates an efficient solution to two fundamental problems in topology optimization of frame structures. The first one involves minimizing structural compliance under linear-elastic equilibrium and weight constraint, while the…
This work considers the infinite-time discounted optimal control problem for continuous time input-affine polynomial dynamical systems subject to polynomial state and box input constraints. We propose a sequence of sum-of-squares (SOS)…
Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the…
We propose a black-box approach to reducing large semidefinite programs to a set of smaller semidefinite programs by projecting to random linear subspaces. We evaluate our method on a set of polynomial optimization problems, demonstrating…
We provide a sparse version of the bounded degree SOS hierarchy BSOS [7] for polynomial optimization problems. It permits to treat large scale problems which satisfy a structured sparsity pattern. When the sparsity pattern satisfies the…
Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…
Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local…
The moment-sum of squares hierarchy by Lasserre has become an established technique for solving polynomial optimization problems. It provides a monotonically increasing series of tight bounds, but has well-known scalability limitations. For…
We study the problem of global maximization of a function f given a finite number of evaluations perturbed by noise. We consider a very weak assumption on the function, namely that it is locally smooth (in some precise sense) with respect…
The behaviour of the moment-sums-of-squares (moment-SOS) hierarchy for polynomial optimal control problems on compact sets has been explored to a large extent. Our contribution focuses on the case of non-compact control sets. We describe a…
Optimizing over the cone of nonnegative polynomials, and its dual counterpart, optimizing over the space of moments that admit a representing measure, are fundamental problems that appear in many different applications from engineering and…
We study a class of polynomial optimization problems with a robust polynomial matrix inequality (PMI) constraint where the uncertainty set itself is defined also by a PMI. These can be viewed as matrix generalizations of semi-infinite…
This paper describes a study of comparison of global and one-dimensional local optimization methods to operating system scheduler tuning. The operating system scheduler we use is the Linux 2.6.23 Completely Fair Scheduler (CFS) running in…