Related papers: A quadratic Grassmann manifold optimization proble…
In this paper, a descent method for nonsmooth multiobjective optimization problems on complete Riemannian manifolds is proposed. The objective functions are only assumed to be locally Lipschitz continuous instead of convexity used in…
We propose a novel Riemannian method for solving the Extreme multi-label classification problem that exploits the geometric structure of the sparse low-dimensional local embedding models. A constrained optimization problem is formulated as…
Quantum annealing provides a promising route for the development of quantum optimization devices, but the usefulness of such devices will be limited in part by the range of implementable problems as dictated by hardware constraints. To…
In a recent work, we presented the reduced Jacobian method (RJM) as an extension of Wolfe's reduced gradient method to multicriteria (multiobjective) optimization problems dealing with linear constraints. This approach reveals that using a…
One of the main bottlenecks in solving combinatorial optimization problems with quantum annealers is the qubit connectivity in the hardware. A possible solution for larger connectivty is minor embedding. This techniques makes the…
This work concerns the global minimization of a prescribed eigenvalue or a weighted sum of prescribed eigenvalues of a Hermitian matrix-valued function depending on its parameters analytically in a box. We describe how the analytical…
Optimization with constraints is a typical problem in quantum physics and quantum information science that becomes especially challenging for high-dimensional systems and complex architectures like tensor networks. Here we use ideas of…
Quantum Annealing (QA) can be used to quickly obtain near-optimal solutions for Quadratic Unconstrained Binary Optimization (QUBO) problems. In QA hardware, each decision variable of a QUBO should be mapped to one or more adjacent qubits in…
The present paper discusses the problem of least-squares over the real symplectic group of matrices Sp(2n,R)$. The least-squares problem may be extended from flat spaces to curved spaces by the notion of geodesic distance. The resulting…
Quartic eigenvalue problem $(\lambda^4 A + \lambda^3 B + \lambda^2C + \lambda D + E)x = \mathbf{0}$ naturally arises e.g. when solving the Orr-Sommerfeld equation in the analysis of the stability of the {Poiseuille} flow, in theoretical…
Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealers that promise to solve certain combinatorial optimization problems of practical relevance faster than their…
This paper presents a novel algorithm integrating global and robust optimization methods to solve continuous non-convex quadratic problems under convex uncertainty sets. The proposed Robust spatial branch-and-bound (RsBB) algorithm combines…
Problems of quadratic optimization in Hilbert space often arise when solving ill-posed problems for differential equations. In this case, the target value of the functional is known. In addition, the structure of the functional allows…
We propose a new algorithm to solve optimization problems of the form $\min f(X)$ for a smooth function $f$ under the constraints that $X$ is positive semidefinite and the diagonal blocks of $X$ are small identity matrices. Such problems…
We propose an inexact optimization algorithm on Riemannian manifolds, motivated by quadratic discrimination tasks in high-dimensional, low-sample-size (HDLSS) imaging settings. In such applications, gradient evaluations are often biased due…
Quantum annealing is a generic solver for optimization problems that uses fictitious quantum fluctuation. The most groundbreaking progress in the research field of quantum annealing is its hardware implementation, i.e., the so-called…
This paper studies the problem of distributed Riemannian optimization over a network of agents whose cost functions are geodesically smooth but possibly geodesically non-convex. Extending a well-known distributed optimization strategy…
In this paper, we present a direct quantum adaptation of the classical shifted power method. The method is very similar to the iterative phase estimation algorithm; however, it does not require any initial estimate of an eigenvector and as…
We give quantum speedups of several general-purpose numerical optimisation methods for minimising a function $f:\mathbb{R}^n \to \mathbb{R}$. First, we show that many techniques for global optimisation under a Lipschitz constraint can be…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…