algorithm design – Optimization Online

A Complete Characterization of Optimal Subgradient Methods for Lipschitz Convex Minimization

Published: 2026/08/01

Nonsmooth Optimization, Semi-definite Programming algorithm design, performance estimation

We consider the design of optimal fixed-step first-order methods for $M$-Lipschitz convex optimization given $\|x_0-x_\star\|\leq D$. Prior works have identified several distinct fixed-step methods, parameterized by a matrix of stepsizes $W$, with the (information-theoretic) minimax optimal rate $MD/\sqrt{N+1}$ of objective gap convergence. We provide a complete characterization of every optimal fixed-step method. Moreover, we show … Read more

Inexactly Smooth Performance Estimation and New Optimized Gradient Methods

Published: 2026/06/07

Convex Optimization, Nonlinear Optimization, Nonsmooth Optimization algorithm design, convex interpolation, inexact smoothness, performance estimation problems

We consider a general class of “inexactly smooth” convex functions, providing a universal model capturing as special cases $L$-smooth, $M$-Lipschitz, and H\”older smooth functions, and any combination thereof. Such functions possess a calculus closely following that of smooth functions. Our main results provide inexactly smooth functions with interpolation theorems that are necessary and sufficient … Read more

Discovering Heuristics with Large Language Models (LLMs) for Mixed-Integer Programs: Single-Machine Scheduling

Published: 2025/10/14

I. Esra Buyuktahtakin Toy

(Mixed) Integer Linear Programming, Combinatorial Optimization, Meta Heuristics algorithm design, Algorithms, Heuristic Discovery, Knowledge Discovery, Large Language Models (LLMs), MIP, optimization, Single Machine Total Tardiness Scheduling

TitleDiscovering Heuristics with Large Language Models (LLMs) for Mixed-Integer Programs: Single-Machine Scheduling Authorsİbrahim Oğuz Çetinkaya^1; İ. Esra Büyüktahtakın^1*; Parshin Shojaee^2; Chandan K. Reddy^2 Affiliations^1 Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, VA, USA^2 Department of Computer Science, Virginia Tech, Arlington, VA, USA Abstract: Our study contributes to the scheduling and combinatorial optimization … Read more

POLO: a POLicy-based Optimization library

Published: 2018/10/10

Convex and Nonsmooth Optimization, Optimization Software Design Principles, Parallel Algorithms algorithm design, asynchronous algorithms, distributed optimization, machine learning, software library

We present POLO — a C++ library for large-scale parallel optimization research that emphasizes ease-of-use, flexibility and efficiency in algorithm design. It uses multiple inheritance and template programming to decompose algorithms into essential policies and facilitate code reuse. With its clear separation between algorithm and execution policies, it provides researchers with a simple and powerful … Read more