Matrix rank minimization issues have recently received a lot of interest in both the mathematics and engineering disciplines. This class of issues is recognized to be NP-hard in general, occurring across a variety of and cross-disciplinary applications.The suggested study examines the issue of minimizing the rank of a matrix over a convex set.The Rank Minimization Problem aka RMP is a computationally NP-hard a challenge that arises in several areas, such as control and system identification, statistics, and signal processing. The research will provide an overview of the issues, as well as their interpretations, applications, and solutions. The emphasis is on method of convex optimization may be utilized to construct heuristic techniques for this issue in specific. The subject of finding the sparest vector in a convex set will be investigated. Many real-world issues in combinatorial optimization and operations research may be represented or approximated using semi-definite programming concerns. SDPs are used in automated control theory to solve linear matrix inequalities. SDPs are a kind of cone programming that can be solved quickly using interior point techniques. Some quantum query complexity issues have recently been stated using semi definite programming.

Rank-Matrix Rank Minimization, Constrained Optimization, Convex Relaxation