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This paper focuses on the decentralized optimization (minimization and saddlepoint) problems with objective functions that satisfy Polyak-{\L}ojasiewiczcondition (PL-condition). The first part of the paper is devoted to theminimization problem of the sum-type cost functions. In order to solve a suchclass of problems, we propose a gradient descent type method with a consensusprojection procedure and the inexact gradient of the objectives. Next, in thesecond part, we study the saddle-point problem (SPP) with a structure of thesum, with objectives satisfying the two-sided PL-condition. To solve such SPP,we propose a generalization of the Multi-step Gradient Descent Ascent methodwith a consensus procedure, and inexact gradients of the objective functionwith respect to both variables. Finally, we present some of the numericalexperiments, to show the efficiency of the proposed algorithm for the robustleast squares problem.

Gradient-Type Methods For Decentralized Optimization Problems With Polyak-{\L}ojasiewicz Condition Over Time-Varying Networks