טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentHallak Nadav
SubjectOn the Minimization over Sparse Symmetric Sets
DepartmentDepartment of Industrial Engineering and Management
Supervisor Professor Amir Beck
Full Thesis textFull thesis text - English Version


Abstract

This thesis treats the problem of minimizing a general continuously differentiable function over symmetric sets under sparsity constraints.

These type of problems are generally hard to solve as the sparsity constraint induces a combinatoric constraint into the problem, rendering the feasible set to be non-convex.

In order to asses and generate possible solutions, we develop necessary optimality conditions with regards to the classical notions of stationarity and coordinate-wise minimum.

Hierarchy between the different types of points is proved, and the structure of the symmetric sets is exploited to efficiently verify and attain points which satisfy optimality conditions of some type.

For that purpose, we begin with researching the orthogonal projection operator onto sparse symmetric sets, concluding with efficient methods for assessing it.

Methods for generating points satisfying optimality conditions of any type are presented, analyzed, and finally tested on specific applications.