arXiv subjects

Fadi Hamad

Publications and source records attributed to Fadi Hamad.

4 recordsLinked to original sources

arXiv2026

An adaptive interior-point method with backtracking line search for convex constrained optimization

Interior-point methods (IPMs) are widely adopted due to their high practical efficiency in solving linear, convex, and nonconvex optimization problems. For convex optimization, this performance is theoretically well-supported: there are strong complexity guarantees for self-concordant barrier setups \cite{nesterov1994interior}, which cover linear and conic optimization. On the other hand, unconstrained convex optimization is well-studied. However, there is limited analysis of constrained convex optimization methods without the self-concordance assumption. We develop and analyze a regularized Newton method with line search applied to the log barrier function in the setting that the objective and constraints are thrice differentiable and have Lipschitz continuous first and second derivatives. Starting from a strictly feasible point, our method finds an $\epsilon$-approximately optimal solution in $\tilde{O}(\epsilon^{-2/3})$ iterations.

math.OC↗

arXiv2024

A simple and practical adaptive trust-region method

We present an adaptive trust-region method for unconstrained optimization that allows inexact solutions to the trust-region subproblems. Our method is a simple variant of the classical trust-region method of \citet{sorensen1982newton}. The method achieves the best possible convergence bound up to an additive log factor, for finding an $\epsilon$-approximate stationary point, i.e., $O( \Delta_f L^{1/2} \epsilon^{-3/2}) + \tilde{O}(1)$ iterations where $L$ is the Lipschitz constant of the Hessian, $\Delta_f$ is the optimality gap, and $\epsilon$ is the termination tolerance for the gradient norm. This improves over existing trust-region methods whose worst-case bound is at least a factor of $L$ worse. We compare our performance with state-of-the-art trust-region (TRU) and cubic regularization (ARC) methods from the GALAHAD library on the CUTEst benchmark set on problems with more than 100 variables. We use fewer function, gradient, and Hessian evaluations than these methods. For instance, our algorithm's median number of gradient evaluations is $23$ compared to $36$ for TRU and $29$ for ARC. Compared to the conference version of this paper \cite{hamad2022consistently}, our revised method includes several practical enhancements. These modifications dramatically improved performance, including an order of magnitude reduction in the shifted geometric mean of wall-clock times. We also show it suffices for the second derivatives to be locally Lipschitz to guarantee that either the minimum gradient norm converges to zero or the objective value tends towards negative infinity, even when the iterates diverge.

math.OC↗

arXiv2024

A consistently adaptive trust-region method

Adaptive trust-region methods attempt to maintain strong convergence guarantees without depending on conservative estimates of problem properties such as Lipschitz constants. However, on close inspection, one can show existing adaptive trust-region methods have theoretical guarantees with severely suboptimal dependence on problem properties such as the Lipschitz constant of the Hessian. For example, TRACE developed by Curtis et al. obtains a $O(\Delta_f L^{3/2} \epsilon^{-3/2}) + \tilde{O}(1)$ iteration bound where $L$ is the Lipschitz constant of the Hessian. Compared with the optimal $O(\Delta_f L^{1/2} \epsilon^{-3/2})$ bound this is suboptimal with respect to $L$. We present the first adaptive trust-region method which circumvents this issue and requires at most $O( \Delta_f L^{1/2} \epsilon^{-3/2}) + \tilde{O}(1)$ iterations to find an $\epsilon$-approximate stationary point, matching the optimal iteration bound up to an additive logarithmic term. Our method is a simple variant of a classic trust-region method and in our experiments performs competitively with both ARC and a classical trust-region method.

math.OC↗

arXiv2023

A supervised generative optimization approach for tabular data

Synthetic data generation has emerged as a crucial topic for financial institutions, driven by multiple factors, such as privacy protection and data augmentation. Many algorithms have been proposed for synthetic data generation but reaching the consensus on which method we should use for the specific data sets and use cases remains challenging. Moreover, the majority of existing approaches are ``unsupervised'' in the sense that they do not take into account the downstream task. To address these issues, this work presents a novel synthetic data generation framework. The framework integrates a supervised component tailored to the specific downstream task and employs a meta-learning approach to learn the optimal mixture distribution of existing synthetic distributions.

cs.LG↗