convex optimization 2lower bounds 2cutting-plane methods 1derivative-free optimization 1first-order oracles 1information complexity 1mixed-integer optimization 1mixed-integer programming 1oracle complexity 1
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math.OC2026
Closing the Oracle-Complexity Gap in Derivative-Free Convex Optimization: A Near-Quadratic Lower Bound from Exact Function Values
Phillip Kerger
The paper proves a near‑quadratic lower bound on the number of exact function‑value queries needed to minimize a convex Lipschitz function over a Euclidean ball, closing a long‑sta…
math.OC2026
Tight Lower Bounds for Binary First-Order Oracles for Convex Optimization
Amitabh Basu, Phillip Kerger, Marco Molinaro
The paper proves that solving mixed-integer convex optimization with bit‑wise first‑order oracles requires a number of bits that grows quadratically with the number of continuous v…
math.OC2024
A Universal Transfer Theorem for Convex Optimization Algorithms Using Inexact First-order Oracles
Phillip Kerger, Marco Molinaro, Hongyi Jiang +1
Given any algorithm for convex optimization that uses exact first-order information (i.e., function values and subgradients), we show how to use such an algorithm to solve the prob…