Reaching Feasibility Quickly for Sets of Linear Constraints
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Finding a feasible solution for a set of linear constraints and bounds is an essential step in many problems, including linear programming. Many linear systems have large numbers of variables and constraints, and the computation time for finding a feasible point can be very large. This thesis proposes an improved projection method for finding a feasible point in linear systems. The method increases the acceleration and improves the direction of movement towards the feasible region. Multiple algorithms developed in this research apply various approaches for the movement acceleration. The thesis also develops an optimization model for finding an optimal set of algorithms having the highest performance in a concurrent implementation. A new presolving technique is introduced which simplifies a linear system before starting the main algorithms. Concurrent computing of the algorithms is proposed for finding a feasible point in large linear systems.
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Copyright © 2018 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. No part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.
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- 2018
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brion-reachingfeasibilityquicklyforsetsoflinear.pdf | 2023-05-05 | Public | Download |