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Mixed-Integer optimization represents a powerful tool for modelling many optimization problems arising from real-world applications. The Feasibility pump is a heuristic for finding feasible solutions to mixed integer linear problems. In this work, we propose a new feasibility pump approach for MIP problems using concave non differentiable penalty functions for measuring solution integrality. Keywords. Mixed integer programming, Concave penalty functions, Frank-Wolfe algorithm, Feasibility Pump. MSC. 90C06, 90C10, 90C11, 90C30, 90C59doi:10.1016/j.dam.2013.06.018 fatcat:puuafw5eqjh2bg3545lflc5gqu