Related papers: Quadrature based optimal iterative methods
Bayesian quadrature is a probabilistic, model-based approach to numerical integration, the estimation of intractable integrals, or expectations. Although Bayesian quadrature was popularised already in the 1980s, no systematic and…
Several different ways exist for approaching hard optimization problems. Mathematical programming techniques, including (integer) linear programming-based methods and metaheuristic approaches, are two highly successful streams for…
Quadratic Unconstrained Binary Optimization (QUBO) is a broad class of optimization problems with many practical applications. To solve its hard instances in an exact way, known classical algorithms require exponential time and several…
Convergence problems in coupled-cluster iterations are discussed, and a new iteration scheme is proposed. Whereas the Jacobi method inverts only the diagonal part of the large matrix of equation coefficients, we invert a matrix which also…
This paper focuses on the design of sequential quadratic optimization (commonly known as SQP) methods for solving large-scale nonlinear optimization problems. The most computationally demanding aspect of such an approach is the computation…
Quadratic assignment problem is one of the great challenges in combinatorial optimization. It has many applications in Operations research and Computer Science. In this paper, the author extends the most-used rounding approach to a…
Recent works have developed new projection-free first-order methods based on utilizing linesearches and normal vector computations to maintain feasibility. These oracles can be cheaper than orthogonal projection or linear optimization…
This paper addresses black-box smooth optimization problems, where the objective and constraint functions are not explicitly known but can be queried. The main goal of this work is to generate a sequence of feasible points converging…
We present a method for optimizing quantum circuits architecture. The method is based on the notion of "quantum comb", which describes a circuit board in which one can insert variable subcircuits. The method allows one to efficiently…
Recent advances in cutting-plane strategies applied to robust optimization problems show that they are competitive with respect to problem reformulations and interior-point algorithms. However, although its application with polyhedral…
An iterative optimization approach that simultaneously minimizes the energy and optimizes the Lagrange multipliers enforcing desired constraints is presented. The method is tested on previously established benchmark systems and it is proved…
Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior…
We describe a novel constructive technique for devising efficient first-order methods for a wide range of large-scale convex minimization settings, including smooth, non-smooth, and strongly convex minimization. The technique builds upon a…
Iterative methods are ubiquitous in large-scale scientific computing applications, and a number of approaches based on meta-learning have been recently proposed to accelerate them. However, a systematic study of these approaches and how…
Many real-world problems rely on finding eigenvalues and eigenvectors of a matrix. The power iteration algorithm is a simple method for determining the largest eigenvalue and associated eigenvector of a general matrix. This algorithm relies…
We propose the use of mixing strategies to accelerate the convergence of the common iterative algorithms utilized in Quantum Optimal Control Theory (QOCT). We show how the non-linear equations of QOCT can be viewed as a "fixed-point"…
The alternating direction method of multipliers (ADMM) has emerged as a powerful technique for large-scale structured optimization. Despite many recent results on the convergence properties of ADMM, a quantitative characterization of the…
In this paper, we study optimal experimental design problems with a broad class of smooth convex optimality criteria, including the classical A-, D- and p th mean criterion. In particular, we propose an interior point (IP) method for them…
Wang tiles enable efficient pattern compression while avoiding the periodicity in tile distribution via programmable matching rules. However, most research in Wang tilings has considered tiling the infinite plane. Motivated by emerging…
This work presents a novel method for task optimization in industrial plants using quantum-inspired tensor network technology. This method obtains the best possible combination of tasks on a set of machines with directed constraints while…