| In recent years,more and more sparse solution problem can be converted into the problem of absolute value equations.Absolute value equations cover many aspects such as linear programming,quadratic programming,and dual matrix countermeasures,and have wide applications in many fields such as finance and engineering.The research on the theoretical direction of the absolute value equation mainly focuses on the explo-ration of the conditions of the mutual transformation between the absolute value equa-tion and the linear complementarity problem,as well as the existence and uniqueness of the absolute value equation solution,the current algorithms for solving absolute value equations include successive linearization methods,semi-smooth Newton algorithms,and smoothed Newton algorithms.Sparsity has now become an important property in many fields,many practical problems have sparse properties,therefore,solving sparse solutions of absolute value equations is an important issue.There are many algorithms for solving absolute value equations at present.However,there are not many research results on the sparse solution of the absolute value equations.Fixed point algorithm is also widely used to solve various optimization problems,it is an effective algorithm to solve many optimization problems.In this paper,the op-erator based on the fixed point algorithm was proposed in order to solve the sparsest so-lution of the NP-hard absolute value equations Ax-|x|=b.The algorithm first relaxed the question to a l1-norm minimization problem,it was further relaxed to an uncon-strained optimization problem by exterior penalty function method,next the fixed-point algorithm of the prox operator was used to solve the approximateoptimization problem.The results of numerical experiment show that the proposed algorithm is very efficient in finding the sparest solution of absolute value equations. |
