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Quality-Diversity (QD) algorithms have emerged as a powerful optimization paradigm with the aim of generating a set of high-quality and diverse solutions. To achieve such a challenging goal, QD algorithms require maintaining a large archive…
Solving differential equations is one of the most computationally expensive problems in classical computing, occupying the vast majority of high-performance computing resources devoted towards practical applications in various fields of…
Mixed Integer Linear Programming (MILP) can be considered the backbone of the modern power system optimization process, with a large application spectrum, from Unit Commitment and Optimal Transmission Switching to verifying Neural Networks…
In this paper we introduce an open-source software package written in C++ for efficiently finding solutions to quadratic programming problems with linear complementarity constraints. These problems arise in a wide range of applications in…
It is well-known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max-cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show…
In computer vision, many problems such as image segmentation, pixel labelling, and scene parsing can be formulated as binary quadratic programs (BQPs). For submodular problems, cuts based methods can be employed to efficiently solve…
Indirect trajectory optimization methods such as Differential Dynamic Programming (DDP) have found considerable success when only planning under dynamic feasibility constraints. Meanwhile, nonlinear programming (NLP) has been the…
While differentiable control has emerged as a powerful paradigm combining model-free flexibility with model-based efficiency, the iterative Linear Quadratic Regulator (iLQR) remains underexplored as a differentiable component. The…
We present a general method, called Qade, for solving differential equations using a quantum annealer. The solution is obtained as a linear combination of a set of basis functions. On current devices, Qade can solve systems of coupled…
Quadratically constrained quadratic programming (QCQP) has long been recognized as a computationally challenging problem, particularly in large-scale or high-dimensional settings where solving it directly becomes intractable. The complexity…
The practical realization of quantum programs that require large-scale qubit systems is hindered by current technological limitations. Distributed Quantum Computing (DQC) presents a viable path to scalability by interconnecting multiple…
This paper introduces HPIPM, a high-performance framework for quadratic programming (QP), designed to provide building blocks to efficiently and reliably solve model predictive control problems. HPIPM currently supports three QP types, and…
Given the limitations of current hardware, the theoretical gains promised by quantum computing remain unrealized across practical applications. But the gap between theory and hardware is closing, assisted by developments in quantum…
The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the well-known satisfiability problem from classical to quantum computation. This problem is shown to be…
Quantum computing (QC) has gained popularity due to its unique capabilities that are quite different from that of classical computers in terms of speed and methods of operations. This paper proposes hybrid models and methods that…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…
Hybrid solvers for combinatorial optimization problems combine the advantages of classical and quantum computing to overcome difficult computational challenges. Although their theoretical performance seems promising, their practical…
In this work, based on the ideas of alternating direction method with multipliers (ADMM) and sequential quadratic programming (SQP), as well as Armijo line search technology, monotone splitting SQP algorithms for two-block nonconvex…
Non-convex quadratically constrained quadratic programming (QCQP) problems have numerous applications in signal processing, machine learning, and wireless communications, albeit the general QCQP is NP-hard, and several interesting special…
Optimizing the architecture of variational quantum circuits (VQCs) is crucial for advancing quantum computing (QC) towards practical applications. Current methods range from static ansatz design and evolutionary methods to machine learned…