Steepest descent methods for multicriteria optimization

By Jörg Fliege, Benar Fux Svaiter. 2000

791 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

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Citations in the corpus

Exploring Example Influence in Continual Learning (2022, positive): “Speciﬁcally, according to the KKT conditions [15], we have Referring to the study from Sener et al. [34], the optimal γ ∗ is easily computed as Thus, the SP Pareto inﬂuence of the training batch can be computed by This process can be seen in Fig.”
Multi-Task Learning as Multi-Objective Optimization (2018, methodology): “MGDA leverages the Karush-Kuhn-Tucker (KKT) conditions, which are necessary for optimality (Fliege and Svaiter, 2000; Schäfﬂer et al., 2002; Désidéri, 2012).”
Newton's Method for Multiobjective Optimization (2009, methodology): “This notion of criticality has already been used in [19] to define a parameter-free steepest descent algorithm for multiobjective optimization.”
Agree to Disagree: Adaptive Ensemble Knowledge Distillation in Gradient Space (2020, methodology): “Inspired by the success of multi-objective optimization (MOO) problem [5, 25, 4, 20], we formulate the ensemble KD as a MOO problem with each objective corresponding to each teacher, which has been applied to recommender system [18], multi-task learning [26, 16], and multi-agent reinforcement…”
Pareto Multi-Task Learning (2019, methodology): “For a constrained multiobjective optimization problem, the Pareto optimality restricted on the feasible region Ω k can be deﬁned as [24]: According to [24, 30], we can ﬁnd a descent direction for this constrained MOP by solving a subproblem similar to the subproblem (3) for the unconstrained case:…”
Using the Averaged Hausdorff Distance as a Performance Measure in Evolutionary Multiobjective Optimization (2012, background): “, [18], [37]), and hence, a sequence of dominating solutions can be generated leading to a (local) solution of the MOP.”