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New methods tackle nonsmooth, nonconvex optimization without derivatives

By PulseAugur Editorial · [1 sources] ·

Researchers have developed new feasible directions methods for optimizing nonsmooth, nonconvex, and constrained problems without relying on derivatives. These methods address the geometric challenge where the feasible direction cone may not be closed at boundary points, hindering the construction of search directions. The proposed framework introduces \"eta-feasible directions\" to ensure finite-direction search even with nonlinear constraints and offers two algorithmic implementations: one using an \"eta-direction oracle\" and another employing a noise-augmented randomization scheme. Both methods aim to control spanning coefficients and feasible step lengths, establishing convergence rates in the proximal directional minimization measure and ensuring that accumulation points are d-stationary. AI

IMPACT Introduces novel mathematical techniques applicable to complex optimization problems in AI and machine learning.

RANK_REASON The cluster contains a single academic paper detailing new optimization methods. [lever_c_demoted from research: ic=1 ai=0.7]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

New methods tackle nonsmooth, nonconvex optimization without derivatives

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The cluster contains a single academic paper detailing new optimization methods. [lever_c_demoted from research: ic=1 ai=0.7]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Dan Greenstein, Nadav Hallak ·

    Randomized and Oracle-Based Feasible Directions Methods for Nonsmooth Nonconvex Constrained Optimization

    arXiv:2611.07691v1 Announce Type: cross Abstract: Minimizing nonsmooth nonconvex objectives over general convex sets using no derivatives of the objective, together with structural access to the constraint set, poses a fundamental geometric difficulty: at boundary points, the fea…

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