arXiv subjects

Ata Keskin

Publications and source records attributed to Ata Keskin.

3 recordsLinked to original sources

arXiv2026

Comparative Evaluation of SDP, SOCP, and QC Convex Relaxations for Large-Scale Market-Based AC Optimal Power Flow

The alternating current optimal power flow (ACOPF) problem is central to modern power system operations, determining how electricity is generated and transmitted to maximize social welfare while respecting physical and operational constraints. However, the nonlinear and non-convex nature of AC power flow equations makes finding globally optimal solutions computationally intractable for large networks. Convex relaxations - including semidefinite programming (SDP), second-order cone programming (SOCP), and quadratic convex (QC) formulations - provide tractable alternatives that can yield provably optimal or near-optimal solutions under appropriate conditions. This paper presents a comprehensive comparative study of multiple ACOPF relaxations applied to market-based welfare maximization. We implement DCOPF, Shor's SDP relaxation (complex and real-valued forms), chordal SDP, Jabr's SOCP relaxation, and QC relaxations in a unified, solver-native framework using the MOSEK Fusion API, eliminating modeling overhead present in high-level frameworks such as CVXPY. To address the practical challenge of missing or overly conservative angle difference bounds required by QC relaxations, we employ quasi-Monte Carlo sampling with Sobol sequences to empirically estimate tighter bounds. We evaluate these relaxations on subnetworks of varying sizes derived from the ARPA-E dataset, systematically comparing solution quality, runtime, and memory consumption. Our results demonstrate the trade-offs between relaxation tightness and computational efficiency, providing practical guidance for selecting appropriate formulations based on network scale and solution requirements.

math.OC↗

arXiv2026

Factor Engine: A Python Library for Systematic Financial Factor Computation and Analysis

Factor Engine is a high-performance, open-source Python library designed for the systematic computation and analysis of financial factors. Built around a modular and extensible API that leverages Python decorators, Factor Engine enables users to define custom factors with ease and integrates seamlessly with the modern data science ecosystem. To assess its practical effectiveness, we compare the mispricing factors computed by Factor Engine to those generated using a reference Stata implementation, finding that both approaches yield highly similar results and comparable performance in backtesting analyses. Furthermore, we experimentally apply these factors within machine learning workflows for trading strategy development, illustrating their practical utility and potential for quantitative finance research.

q-fin.CP↗

arXiv2023

A Formalization of Martingales in Isabelle/HOL

This thesis presents a formalization of martingales in arbitrary Banach spaces using Isabelle/HOL. We begin by examining formalizations in prominent proof repositories and extend the definition of the conditional expectation operator from the real numbers to general Banach spaces. The current formalization of conditional expectation in the Isabelle library is limited to real-valued functions. To overcome this limitation, we use measure theoretic arguments to construct the conditional expectation in Banach spaces using suitable limits of simple functions. Subsequently, we define stochastic processes and introduce the concepts of adapted, progressively measurable and predictable processes using suitable locale definitions. We show the relation $$\text{adapted} \supseteq \text{progressive} \supseteq \text{predictable}$$ Furthermore, we show that progressive measurability and adaptedness are equivalent when the indexing set is discrete. We pay special attention to predictable processes in discrete-time, showing that $(X_n)_{n \in \mathbb{N}}$ is predictable if and only if $(X_{n + 1})_{n \in \mathbb{N}}$ is adapted. We rigorously define martingales, submartingales, and supermartingales, presenting their first consequences and corollaries. Discrete-time martingales are given special attention in the formalization. In every step of our formalization, we make extensive use of the powerful locale system of Isabelle. The formalization further contributes by generalizing concepts in Bochner integration by extending their application from the real numbers to arbitrary Banach spaces equipped with a second-countable topology. Induction schemes for integrable simple functions on Banach spaces are introduced. Additionally, we formalize a powerful result called the "Averaging Theorem" which allows us to show that densities are unique in Banach spaces.

cs.LO↗