Particle Swarm Optimization for Absolute Value Equations
نویسنده
چکیده
We investigate the NP-hard absolute value equation (AVE) Au |u| = b, where A is an arbitrary square matrix. In this paper, we present a smoothing method for the AVE. First, we replace the absolute value function by a smooth one, called aggregate function. With this smoothing technique, we formulate the non-smooth AVE as a smooth nonlinear equations, furthermore, an unconstrained differentiable optimization problem. Then we adopt Particle Swarm Optimization (PSO) to AVE. The numerical experiments show that the proposed algorithm is effective in dealing with the AVE.
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