<ul><li>The imbalances and conditioning of the objective functions influence the performance of first-order methods for multiobjective optimization problems (MOPs).</li><li>To balance per-iteration cost and better curvature exploration, a Barzilai-Borwein descent method with variable metrics (BBDMO_VM) is proposed.</li><li>BBDMO_VM employs a variable metric in the direction-finding subproblems to explore the curvature of all objectives and mitigate the effect of imbalances.</li><li>Comparative numerical results confirm the efficiency of the proposed BBDMO_VM method for large-scale and ill-conditioned multiobjective optimization problems.</li><li>A nonmonotone proximal quasi-Newton method for unconstrained convex multiobjective composite optimization problems is proposed.</li><li>The method employs a nonmonotone line search and converges to a Pareto optimal solution.</li><li>Numerical experiments show the effectiveness of the proposed algorithm on a set of test problems.</li></ul>

Best Examples in Multiobjective Optimization part8(Machine Learning 2024)

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