Related papers: Optimal Scaling Quantum Interior Point Method for …
Hierarchical least-squares programs with linear constraints (HLSP) are a type of optimization problem very common in robotics. Each priority level contains an objective in least-squares form which is subject to the linear constraints of the…
Integer linear programming (ILP) encompasses a very important class of optimization problems that are of great interest to both academia and industry. Several algorithms are available that attempt to explore the solution space of this class…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
We present an efficient, nearly optimal quantum algorithm for solving linear matrix differential equations, with applications to the simulation of open quantum systems and beyond. For unitary or dissipative dynamics, the algorithm computes…
The efficient computation of parametric solution sensitivities is a key challenge in the integration of learning-enhanced methods with nonlinear model predictive control (MPC), as their availability is crucial for many learning algorithms.…
Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an $N\times{N}$…
The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton's method. There is a trade-off between solving Newton systems…
We propose Newton-PIPG, an efficient method for solving quadratic programming (QP) problems arising in optimal control, subject to additional set constraints. Newton-PIPG integrates the Proportional-Integral Projected Gradient (PIPG) method…
Quantum approximate optimization is one of the promising candidates for useful quantum computation, particularly in the context of finding approximate solutions to Quadratic Unconstrained Binary Optimization (QUBO) problems. However, the…
The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, i.e., the set of all Pareto optimal solutions, where no objective can be improved without…
Quantum machine learning (QML) is promising for potential speedups and improvements in conventional machine learning (ML) tasks (e.g., classification/regression). The search for ideal QML models is an active research field. This includes…
When an iterative method is applied to solve the linear equation system in interior point methods (IPMs), the attention is usually placed on accelerating their convergence by designing appropriate preconditioners, but the linear solver is…
In a recent study (Ref. [1]), quantum annealing was reported to exhibit a scaling advantage for approximately solving Quadratic Unconstrained Binary Optimization (QUBO). However, this claim critically depends on the choice of classical…
Solving optimization problems is the key to decision making in many real-life analytics applications. However, the coefficients of the optimization problems are often uncertain and dependent on external factors, such as future demand or…
We study the problem of solving linear program in the streaming model. Given a constraint matrix $A\in \mathbb{R}^{m\times n}$ and vectors $b\in \mathbb{R}^m, c\in \mathbb{R}^n$, we develop a space-efficient interior point method that…
Nonlinear Model Predictive Control (NMPC) is a general and flexible control approach, used in many industrial contexts, and is based on the online solution of a nonlinear optimization problem. This operation requires in general a high…
We present a quantum interior-point method (IPM) for second-order cone programming (SOCP) that runs in time $\widetilde{O} \left( n\sqrt{r} \frac{\zeta \kappa}{\delta^2} \log \left(1/\epsilon\right) \right)$ where $r$ is the rank and $n$…
The Quantum Approximate Optimisation Algorithm (QAOA) is a widely studied quantum-classical iterative heuristic for combinatorial optimisation. While QAOA targets problems in complexity class NP, the classical optimisation procedure…
In the last fifteen years a significant progress was achieved by considering an entropic relaxation of the classical multi-partite optimal transport problem (MPOTP). The entropic relaxation gives rise to the rescaling problem of a given…
The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here,…