Abstract
In this work we consider an extension of the projected gradient method (PGM) to constrained multiobjective problems. The projected gradient scheme for multiobjective optimization proposed by Grana Drummond and Iusem and analyzed by Fukuda and Grana Drummond is extended to include a nonmonotone line search based on the average of the successive previous functions values instead of the traditional Armijo-like rules. Under standard assumptions, stationarity of the accumulation points is established. Moreover, under standard convexity assumptions, we prove full convergence to weakly Pareto optimal solutions of any sequence produced by the proposed algorithm.
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