Second and Higher-Order Conditions for Solutions to Constrained Optimisation Problems and Nonlinear Quantum Computation

Kooper De Lacy

doi:10.26182/5df9c51c81313

Second and Higher-Order Conditions for Solutions to Constrained Optimisation Problems and Nonlinear Quantum Computation

Kooper De Lacy

School of Physics, Mathematics and Computing

Research output: Thesis › Master's Thesis

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Abstract

We develop necessary conditions for a solution to any constrained optimisation problem. Our conditions are stronger than previous results and provide meaningful information on nondifferentiable surfaces defined by the constraints. These results are useful to create numerical optimisers.
We consider a model of quantum computation able to take advantage of linear and nonlinear quantum behaviours. This leads to the creation of several new algorithms, each solving search or counting problems. We show that solving search problems using classical fields provides a square root speedup over classical computation.

Original language	English
Qualification	Masters
Awarding Institution	The University of Western Australia
Supervisors/Advisors	Noakes, Lyle, Supervisor Wang, Jingbo, Supervisor
Thesis sponsors	Australian Government Research Training Program
Award date	12 Nov 2019
DOIs	https://doi.org/10.26182/5df9c51c81313
Publication status	Unpublished - 2019

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THESIS - MASTER BY RESEARCH - DE LACY Kooper Jon - 2019
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AB - We develop necessary conditions for a solution to any constrained optimisation problem. Our conditions are stronger than previous results and provide meaningful information on nondifferentiable surfaces defined by the constraints. These results are useful to create numerical optimisers. We consider a model of quantum computation able to take advantage of linear and nonlinear quantum behaviours. This leads to the creation of several new algorithms, each solving search or counting problems. We show that solving search problems using classical fields provides a square root speedup over classical computation.

KW - Constrained optimisation

KW - singularities

KW - differential geometry

KW - quantum computation

KW - graph similiarity

KW - search problems

U2 - 10.26182/5df9c51c81313

DO - 10.26182/5df9c51c81313

M3 - Master's Thesis

ER -

Second and Higher-Order Conditions for Solutions to Constrained Optimisation Problems and Nonlinear Quantum Computation

Abstract

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