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Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
In recent years, numerous vision and learning tasks have been (re)formulated as nonconvex and nonsmooth programmings(NNPs). Although some algorithms have been proposed for particular problems, designing fast and flexible optimization…
Recent hardware demonstrations and advances in circuit compilation have made quantum computing with higher-dimensional systems (qudits) on near-term devices an attractive possibility. Some problems have more natural or optimal encodings…
We introduce parity quantum optimization with the aim of solving optimization problems consisting of arbitrary $k$-body interactions and side conditions using planar quantum chip architectures. The method introduces a decomposition of the…
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…
Recent advances in quantum computing and the increasing availability of quantum hardware have substantially enhanced the practical relevance of quantum approaches to discrete optimization. Among these, the Quadratic Unconstrained Binary…
Differentiable optimization has attracted significant research interest, particularly for quadratic programming (QP). Existing approaches for differentiating the solution of a QP with respect to its defining parameters often rely on…
In this paper, we concentrate on a particular category of quadratically constrained quadratic programming (QCQP): nonconvex QCQP with one equality constraint. This type of QCQP problem optimizes a quadratic objective under a fixed…
The growing demand for solving large-scale, data-intensive linear and conic optimization problems, particularly in applications such as artificial intelligence and machine learning, has highlighted the limitations of classical interior…
In this paper, we develop a way to encode several NP-Complete problems in Abstract Argumentation to Quadratic Unconstrained Binary Optimization (QUBO) problems. In this form, a solution for a QUBO problem involves minimizing a quadratic…
We propose a sequential quadratic programming (SQP) algorithm for inequality constrained optimization that is robust to the presence of bounded noise in function and derivative evaluations. We cover the case where constraint evaluations…
In cancer radiotherapy, the standard formulation of the optimal fractionation problem based on the linear-quadratic dose-response model is a non-convex quadratically constrained quadratic program (QCQP). An optimal solution for this QCQP…
Many computational problems involve optimization over discrete variables with quadratic interactions. Known as discrete quadratic models (DQMs), these problems in general are NP-hard. Accordingly, there is increasing interest in encoding…
Quantum Annealing (QA) can efficiently solve combinatorial optimization problems whose objective functions are represented by Quadratic Unconstrained Binary Optimization (QUBO) formulations. For broader applicability of QA, quadratization…
To evaluate a quantum circuit on a quantum processor, one must find a mapping from circuit qubits to processor qubits and plan the instruction execution while satisfying the processor's constraints. This is known as the qubit mapping and…
A novel algorithm to solve the quadratic programming problem over ellipsoids is proposed. This is achieved by splitting the problem into two optimisation sub-problems, quadratic programming over a sphere and orthogonal projection. Next, an…
In building a quantum information processor (QIP), the challenge is to coherently control a large quantum system well enough to perform an arbitrary quantum algorithm and to be able to correct errors induced by decoherence. Nuclear magnetic…
We consider the exact solution of problem $(QP)$ that consists in minimizing a quadratic function subject to quadratic constraints. Starting from the classical convex relaxation that uses the McCormick's envelopes, we introduce 12…
This manuscript develops a new framework to analyze and design iterative optimization algorithms built on the notion of Integral Quadratic Constraints (IQC) from robust control theory. IQCs provide sufficient conditions for the stability of…
In this paper, we propose a framework for fast trajectory planning for unmanned aerial vehicles (UAVs). Our framework is reformulated from an existing bilevel optimization, in which the lower-level problem solves for the optimal trajectory…