Related papers: Equilibrium search algorithm of a perturbed quasi-…
One of the most important optimality conditions to aid to solve a vector optimization problem is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient optimality…
Optimizing high-degree of freedom robotic manipulators requires searching complex, high-dimensional configuration spaces, a task that is computationally challenging for classical methods. This paper introduces a quantum native framework…
We describe a simple quantum algorithm to simulate time-dependent Hamiltonian, extending the methodology of quantum signal processing. The framework achieves optimal scaling up to some factor with respect to other parameters, and nearly…
We address the characterization of classical fractional random noise via quantum probes. In particular, we focus on estimation and discrimination problems involving the fractal dimension of the trajectories of a system subject to fractional…
In this paper we present a novel quantum algorithm, namely the quantum grid search algorithm, to solve a special search problem. Suppose $ k $ non-empty buckets are given, such that each bucket contains some marked and some unmarked items.…
In the study of equilibrium solutions for partial differential equations there are so many equilibria that one cannot hope to find them all. Therefore one usually concentrates on finding individual branches of equilibrium solutions. On the…
We propose an unconstrained optimization method based on the well-known primal-dual hybrid gradient (PDHG) algorithm. We first formulate the optimality condition of the unconstrained optimization problem as a saddle point problem. We then…
In the first-order query model for zero-sum $K\times K$ matrix games, players observe the expected pay-offs for all their possible actions under the randomized action played by their opponent. This classical model has received renewed…
We adopt the integral definition of the fractional Laplace operator and analyze an optimal control problem for a fractional semilinear elliptic partial differential equation (PDE); control constraints are also considered. We establish the…
A practical and simple stable method for calculating Fourier integrals is proposed, effective both at low and at high frequencies. An approach based on the fruitful idea of Levin, to use of the collocation method to approximate the slowly…
We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted…
In this paper, we study the equality constrained nonlinear least squares problem, where the Jacobian matrices of the objective function and constraints are unavailable or expensive to compute. We approximate the Jacobian matrices via…
A new efficient approach for searching three-body periodic equal-mass collisionless orbits passing through Eulerian configuration is presented. The approach is based on a symmetry property of the solutions at the half period. Depending on…
In a recent work, Esmer et al. describe a simple method - Approximate Monotone Local Search - to obtain exponential approximation algorithms from existing parameterized exact algorithms, polynomial-time approximation algorithms and, more…
Via a random construction we establish necessary conditions for $L^p(\ell^q)$ inequalities for certain families of operators arising in harmonic analysis. In particular we consider dilates of a convolution kernel with compactly supported…
Unstructured search remains as one of the significant challenges in computer science, as classical search algorithms become increasingly impractical for large-scale systems due to their linear time complexity. Quantum algorithms, notably…
This work tackles a class of optimization problems in which fixing some well-chosen combinations of the variables makes the problem substantially easier to solve. We consider that the variables space may be partitioned into subsets that fix…
We present a quantum algorithmic routine that extends the realm of Grover-based heuristics for tackling combinatorial optimization problems with arbitrary efficiently computable objective and constraint functions. Building on previously…
In this paper we present a sufficient condition for the existence of a solution for an equilibrium problem on an Hadamard manifold and under suitable assumptions on the sectional curvature, we propose a framework for the convergence…
We hereby study the stability of a massless probe orbiting around an oblate central body (planet or planetary satellite) perturbed by a third body, assumed to lie in the equatorial plane (Sun or Jupiter for example) using an Hamiltonian…