Reference number : GC-2017-Q1-02461, amendment number : , agreement type : G, recipient legal name : Chang, Xiao-Wen (McGill University)|Chang, Xiao-Wen (Université McGill), recipient country : CA, recipient province : nan, recipient city : Quebec|Québec, recipient postal code : nan, program name english : Discovery Grants Program - Individual, program name french : Programme de subventions à la découverte - individuelles, program purpose english : In many applications such as communications, control, finance, global navigation satellite systems, operations research, one needs to estimate an unknown integer parameter vector in a linear or linearized model. A typical approach is to solve an integer least squares problem. Sometimes a sparse solution is needed, and then one solves or approximately solves an optimization problem, such as an integer least squares problem with l 0 or l 1 norm regularization - this is an emerging area which has great potential in such applications. The difficulty is that often the optimization problems in this area are NP-hard. However it is possible to find optimal solutions within reasonable time for some problems of moderate size arising in many practical applications. The main objectives of this proposal are to develop fast algorithms and the relevant software for solving these integer least squares related problems. Specifically we will develop efficient search algorithms. To make the search process faster, we will develop effective and efficient reduction strategies and lower bounds for those optimization problems. The potential of reduction strategies to improve the search speed and success probability of some sub-optimal estimators has not been realized or fully realized. Our proposed research is expected to have significant impacts on the development of algorithms in this area, especially on the development of reduction algorithms. The resulting algorithms and software will greatly benefit people in applied fields and their related industries., program purpose french : In many applications such as communications, control, finance, global navigation satellite systems, operations research, one needs to estimate an unknown integer parameter vector in a linear or linearized model. A typical approach is to solve an integer least squares problem. Sometimes a sparse solution is needed, and then one solves or approximately solves an optimization problem, such as an integer least squares problem with l 0 or l 1 norm regularization - this is an emerging area which has great potential in such applications. The difficulty is that often the optimization problems in this area are NP-hard. However it is possible to find optimal solutions within reasonable time for some problems of moderate size arising in many practical applications. The main objectives of this proposal are to develop fast algorithms and the relevant software for solving these integer least squares related problems. Specifically we will develop efficient search algorithms. To make the search process faster, we will develop effective and efficient reduction strategies and lower bounds for those optimization problems. The potential of reduction strategies to improve the search speed and success probability of some sub-optimal estimators has not been realized or fully realized. Our proposed research is expected to have significant impacts on the development of algorithms in this area, especially on the development of reduction algorithms. The resulting algorithms and software will greatly benefit people in applied fields and their related industries., agreement title english : Numerical Methods for Integer Parameter Estimation and Applications, agreement title french : Numerical Methods for Integer Parameter Estimation and Applications, agreement number : RGPIN, agreement value : 210000.0, agreement start date : 2017-05-10, agreement end date : nan, description english : nan, description french : nan, expected results english : nan, expected results french : nan, additional information english : Grant or Award spanning more than one fiscal year. (2017-2018 to 2022-2023), additional information french : Subvention ou bourse octroyée s'appliquant à plus d'un exercice financier. (2017-2018 à 2022-2023), owner organization : nserc-crsng, owner organization title : Natural Sciences and Engineering Research Council of Canada | Conseil de recherches en sciences naturelles et en génie du Canada