Cristóbal Guzmán

activity

20242026

most citedHow to DP-fy Your Data: A Practical Guide to Generating Synthetic Data With Differential Privacy

1 citations · 1 across the 15 of their papers we have counts for

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7 papers · 1 filter

math.OC2026

Near-Optimal Acceleration for Smooth $ℓ_{p}$ / $ℓ_{q}$ Nondual Convex First-Order Oracle Optimization

David Martínez-Rubio, Brian Bullins, Cristóbal Guzmán +1

We study the optimization of convex objectives with $(L, κ - 1)$ -Hölder-continuous gradients in $ℓ_{q}$ over $R B_{p}^{d}$ , $1 < κ \leq 2$ . (MG26) provides selectors with a movement bound fo…

math.OC2026

Stable Movement for Nondual Lipschitz Convex Optimization: Efficiency and Nearly Optimal Oracle Rates

David Martínez-Rubio, Cristóbal Guzmán

We study efficient algorithms for realizing the first-order oracle complexity of optimization of $G$ -Lipschitz convex functions with respect to the $ℓ_{q}$ -norm over an $\ell_{p…

math.OC2026

The First-Order Oracle Complexity of Lipschitz Convex Optimization in Nondual Settings

David Martínez-Rubio, Brian Bullins, Cristóbal Guzmán +1

We study first-order black-box convex optimization over an $ℓ_{p}$ -ball for objectives Lipschitz in the $ℓ_{q}$ -norm, solving in the affirmative the nonsmooth version of the COLT…

math.OC2026

Oracle Complexity of Stochastic Fixed-Point Equations with Nonexpansive Maps

Jelena Diakonikolas, Cristóbal Guzmán, David Martínez-Rubio

We study the oracle complexity of computing a point with small fixed-point residual $∥ T (x) - x ∥ \leq ε$ , for a general norm $∥ \cdot ∥$ and a self-map $T$ of a compact convex set.…

math.OC2024

Non-Euclidean High-Order Smooth Convex Optimization

Juan Pablo Contreras, Cristóbal Guzmán, David Martínez-Rubio

We develop algorithms for the optimization of convex objectives that have Hölder continuous $q$ -th derivatives by using a $q$ -th order oracle, for any $q \geq 1$ . Our algorithms wo…

math.OC2024

Optimization on a Finer Scale: Bounded Local Subgradient Variation Perspective

Jelena Diakonikolas, Cristóbal Guzmán

We initiate the study of nonsmooth optimization problems under bounded local subgradient variation, which postulates bounded difference between (sub)gradients in small local region…

math.OC2024

Mirror Descent Algorithms with Nearly Dimension-Independent Rates for Differentially-Private Stochastic Saddle-Point Problems

Tomás González, Cristóbal Guzmán, Courtney Paquette

We study the problem of differentially-private (DP) stochastic (convex-concave) saddle-points in the $ℓ_{1}$ setting. We propose $(ε, δ)$ -DP algorithms based on stochast…

Near-Optimal Acceleration for Smooth ℓp​ / ℓq​ Nondual Convex First-Order Oracle Optimization

Stable Movement for Nondual Lipschitz Convex Optimization: Efficiency and Nearly Optimal Oracle Rates

The First-Order Oracle Complexity of Lipschitz Convex Optimization in Nondual Settings

Oracle Complexity of Stochastic Fixed-Point Equations with Nonexpansive Maps

Non-Euclidean High-Order Smooth Convex Optimization

Optimization on a Finer Scale: Bounded Local Subgradient Variation Perspective

Mirror Descent Algorithms with Nearly Dimension-Independent Rates for Differentially-Private Stochastic Saddle-Point Problems

Near-Optimal Acceleration for Smooth $ℓ_{p}$ / $ℓ_{q}$ Nondual Convex First-Order Oracle Optimization