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New Research Explores Optimality Certificates Beyond Polynomials

By PulseAugur Editorial · [2 sources] ·

A new research paper explores certificates of positivity and optimality for learning problems where objectives and constraints are not limited to polynomials. The work isolates an axiomatic core of Fischer's constructive Positivstellensätze, proving theorems for abstract function algebras over ordered fields. This framework distinguishes between objective/constraint functions built from continuous or definable operations and the auxiliary primitives used for certificate construction, which must meet specific scalar and closure axioms. The paper provides instances over various function algebras, including those not closed under square roots, and analyzes complexity related to term length and computation graphs. AI

IMPACT This research could advance theoretical underpinnings for complex optimization problems in machine learning.

RANK_REASON The cluster contains an academic paper published on arXiv.

Read on Hugging Face Daily Papers →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

New Research Explores Optimality Certificates Beyond Polynomials

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COVERAGE [2]

  1. arXiv cs.AI TIER_1 English(EN) · Nayoon Kim, Allen Gehret, Shenyuan Ma, Jakub Marecek ·

    When Can One Obtain Certificates of Optimality Using Positivstellensaetze?

    arXiv:2609.08736v1 Announce Type: new Abstract: We study certificates of positivity and optimality for learning problems whose objectives and constraints need not be polynomial. We isolate an axiomatic core of Fischer's constructive strict and weak Positivstellens\"{a}tze and pro…

  2. Hugging Face Daily Papers TIER_1 English(EN) ·

    When Can One Obtain Certificates of Optimality Using Positivstellensaetze?

    We study certificates of positivity and optimality for learning problems whose objectives and constraints need not be polynomial. We isolate an axiomatic core of Fischer's constructive strict and weak Positivstellensätze and prove the resulting theorems for abstract function alge…

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