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Continuous search problems (CSPs), which involve finding solutions within a continuous domain, frequently arise in fields such as optimization, physics, and engineering. Unlike discrete search problems, CSPs require navigating an…
Real-world optimization problems must undergo a series of transformations before becoming solvable on current quantum hardware. Even for a fixed problem, the number of possible transformation paths -- from industry-relevant formulations…
A sparse linear programming (SLP) problem is a linear programming problem equipped with a sparsity (or cardinality) constraint, which is nonconvex and discontinuous theoretically and generally NP-hard computationally due to the…
The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the…
We describe Superstaq, a quantum software platform that optimizes the execution of quantum programs by tailoring to underlying hardware primitives. For benchmarks such as the Bernstein-Vazirani algorithm and the Qubit Coupled Cluster…
Semidefinite programs (SDPs) play a crucial role in control theory, traditionally as a computational tool. Beyond computation, the duality theory in convex optimization also provides valuable analytical insights and new proofs of classical…
This paper presents a stabilized sequential quadratic programming (SQP) method for solving optimization problems in Banach spaces. The optimization problem considered in this study has a general form that enables us to represent various…
We propose a new approach to utilize quantum computers for binary linear programming (BLP), which can be extended to general integer linear programs (ILP). Quantum optimization algorithms, hybrid or quantum-only, are currently general…
Despite major advancements in nonlinear programming (NLP) and convex relaxations, most system operators around the world still predominantly use some form of linear programming (LP) approximation of the AC power flow equations. This is…
In this paper, we study the problem of optimizing a linear program whose variables are the answers to a conjunctive query. For this we propose the language LP(CQ) for specifying linear programs whose constraints and objective functions…
Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…
We provide several quantum algorithms for continuous optimization that do not require gradient estimation. Instead, we encode the optimization problem into the dynamics of a physical system and coherently simulate the time evolution. We…
Efficient task scheduling is paramount in parallel programming on multi-core architectures, where tasks are fundamental computational units. QR factorization is a critical sub-routine in Sequential Least Squares Quadratic Programming…
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…
This paper investigates the relation between sequential convex programming (SCP) as, e.g., defined in [24] and DC (difference of two convex functions) programming. We first present an SCP algorithm for solving nonlinear optimization…
Semidefinite programming (SDP) problems are challenging to solve because of their high dimensionality. However, solving sparse SDP problems with small tree-width are known to be relatively easier because: (1) they can be decomposed into…
This paper develops new semidefinite programming (SDP) relaxation techniques for two classes of mixed binary quadratically constrained quadratic programs (MBQCQP) and analyzes their approximation performance. The first class of problem…
Semidefinite relaxations are widely used to compute upper bounds on the objective of optimization problems involving noncommutative polynomials. Such optimization problems are prevalent in quantum information. We present an algorithm able…
We introduce a novel method for clustering using a semidefinite programming (SDP) relaxation of the Max k-Cut problem. The approach is based on a new methodology for rounding the solution of an SDP relaxation using iterated linear…
Similarity-based Logic Programming (briefly, SLP ) has been proposed to enhance the LP paradigm with a kind of approximate reasoning which supports flexible information retrieval applications. This approach uses a fuzzy similarity relation…