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Variable order structures model situations in which the comparison betweentwo points depends on a point-to-cone map. In this paper, an inexact projectedgradient method for solving smooth constrained vector optimization problems onvariable ordered spaces is presented. It is shown that every accumulation pointof the generated sequence satisfies the first order necessary optimalitycondition. The convergence of all accumulation points to a weakly efficientpoint is established under suitable convexity assumptions for the objectivefunction. The convergence results are also derived in the particular case inwhich the problem is unconstrained and if exact directions are taken as descentdirections. Furthermore, we investigate the application of the proposed methodto optimization models where the domain of the variable order map and theobjective function are the same. In this case, similar concepts and convergenceresults are presented. Finally, some computational experiments designed toillustrate the behavior of the proposed inexact methods versus the exact ones(in terms of CPU time) are performed.

An inexact strategy for the projected gradient algorithm in vector optimization problems on variable ordered spaces