arXiv subjects

Figen Oztoprak

Publications and source records attributed to Figen Oztoprak.

8 recordsLinked to original sources

arXiv2026

Robust Airfoil Design Optimization via a Bilevel Model-Based Methodology

We propose GLORO, a bilevel solution methodology for robust optimization involving expensive function evaluations. The methodology is carefully designed to achieve satisfactory optimization results in a computationally efficient manner. It is based on Gaussian Process surrogates in the parameter space for approximate computations of the objective / constraints of the robust optimization problem via Bayesian optimization (lower level), and local models constructed in the variable space using these approximate evaluations (upper level). Both the use of Bayesian optimization (in parameter space) and the use of local models (in variable space) are motivated by the idea of guiding the expensive function evaluations to the regions of interest for the optimization process. The methodological work is motivated by and tested on a robust airfoil design optimization problem. This application focuses on the RAE2822 airfoil, optimizing its shape to ensure a robust lift-to-drag ratio under operational uncertainties in Mach number and angle of attack.

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arXiv2026

Optimization with Dynamic Constraint Learning (DCL)

We propose Dynamic Constraint Learning (DCL), a data-driven framework for constrained optimization when constraint functions are unknown and cannot be queried during optimization. At each iteration, the method learns a local surrogate from nearby data and solves a subproblem within a data-supported trust region. Compared with offline global constraint learning, the approach uses local surrogates that adapt to the data distribution during optimization and can achieve solution quality comparable to that of global models while using simpler local models and smaller optimization subproblems. We demonstrate the performance of DCL on a synthetic test problem and two case studies from the literature.

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arXiv2026

A Noise Tolerant SQP Algorithm for Inequality Constrained Optimization

We propose a sequential quadratic programming (SQP) algorithm for inequality constrained optimization that is robust to the presence of bounded noise in function and derivative evaluations. We cover the case where constraint evaluations contain noise as well as the objective. The proposed algorithm is a line search SQP method with relaxations to deal with noise. We study the effect of noise on the global convergence behavior of the algorithm. We implement the algorithm with noise-aware quasi-Newton updates, and numerically observe that the algorithm can achieve accuracy proportional to the noise level and problem-dependent parameters, as suggested by the theory.

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arXiv2024

Bolstering Stochastic Gradient Descent with Model Building

Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are fine-tuned for the application at hand. Although this tuning process can require large computational costs, recent work has shown that these costs can be reduced by line search methods that iteratively adjust the step length. We propose an alternative approach to stochastic line search by using a new algorithm based on forward step model building. This model building step incorporates second-order information that allows adjusting not only the step length but also the search direction. Noting that deep learning model parameters come in groups (layers of tensors), our method builds its model and calculates a new step for each parameter group. This novel diagonalization approach makes the selected step lengths adaptive. We provide convergence rate analysis, and experimentally show that the proposed algorithm achieves faster convergence and better generalization in well-known test problems. More precisely, SMB requires less tuning, and shows comparable performance to other adaptive methods.

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arXiv2021

Constrained Optimization in the Presence of Noise

The problem of interest is the minimization of a nonlinear function subject to nonlinear equality constraints using a sequential quadratic programming (SQP) method. The minimization must be performed while observing only noisy evaluations of the objective and constraint functions. In order to obtain stability, the classical SQP method is modified by relaxing the standard Armijo line search based on the noise level in the functions, which is assumed to be known. Convergence theory is presented giving conditions under which the iterates converge to a neighborhood of the solution characterized by the noise level and the problem conditioning. The analysis assumes that the SQP algorithm does not require regularization or trust regions. Numerical experiments indicate that the relaxed line search improves the practical performance of the method on problems involving uniformly distributed noise. One important application of this work is in the field of derivative-free optimization, when finite differences are employed to estimate gradients.

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arXiv2021

On the Numerical Performance of Derivative-Free Optimization Methods Based on Finite-Difference Approximations

The goal of this paper is to investigate an approach for derivative-free optimization that has not received sufficient attention in the literature and is yet one of the simplest to implement and parallelize. It consists of computing gradients of a smoothed approximation of the objective function (and constraints), and employing them within established codes. These gradient approximations are calculated by finite differences, with a differencing interval determined by the noise level in the functions and a bound on the second or third derivatives. It is assumed that noise level is known or can be estimated by means of difference tables or sampling. The use of finite differences has been largely dismissed in the derivative-free optimization literature as too expensive in terms of function evaluations and/or as impractical when the objective function contains noise. The test results presented in this paper suggest that such views should be re-examined and that the finite-difference approach has much to be recommended. The tests compared NEWUOA, DFO-LS and COBYLA against the finite-difference approach on three classes of problems: general unconstrained problems, nonlinear least squares, and general nonlinear programs with equality constraints.

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arXiv2015

A Second-Order Method for Convex $\ell_1$-Regularized Optimization with Active Set Prediction

We describe an active-set method for the minimization of an objective function $ϕ$ that is the sum of a smooth convex function and an $\ell_1$-regularization term. A distinctive feature of the method is the way in which active-set identification and {second-order} subspace minimization steps are integrated to combine the predictive power of the two approaches. At every iteration, the algorithm selects a candidate set of free and fixed variables, performs an (inexact) subspace phase, and then assesses the quality of the new active set. If it is not judged to be acceptable, then the set of free variables is restricted and a new active-set prediction is made. We establish global convergence for our approach, and compare the new method against the state-of-the-art code LIBLINEAR.

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arXiv2013

An Inexact Successive Quadratic Approximation Method for Convex L-1 Regularized Optimization

We study a Newton-like method for the minimization of an objective function that is the sum of a smooth convex function and an l-1 regularization term. This method, which is sometimes referred to in the literature as a proximal Newton method, computes a step by minimizing a piecewise quadratic model of the objective function. In order to make this approach efficient in practice, it is imperative to perform this inner minimization inexactly. In this paper, we give inexactness conditions that guarantee global convergence and that can be used to control the local rate of convergence of the iteration. Our inexactness conditions are based on a semi-smooth function that represents a (continuous) measure of the optimality conditions of the problem, and that embodies the soft-thresholding iteration. We give careful consideration to the algorithm employed for the inner minimization, and report numerical results on two test sets originating in machine learning.

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