arXiv subjects

Shima Dezfulian

Publications and source records attributed to Shima Dezfulian.

3 recordsLinked to original sources

arXiv2025

An Interior-Point Algorithm for Continuous Nonlinearly Constrained Optimization with Noisy Function and Derivative Evaluations

An algorithm based on the interior-point methodology for solving continuous nonlinearly constrained optimization problems is proposed, analyzed, and tested. The distinguishing feature of the algorithm is that it presumes that only noisy values of the objective and constraint functions and their first-order derivatives are available. The algorithm is based on a combination of a previously proposed interior-point algorithm that allows inexact subproblem solutions and recently proposed algorithms for solving bound- and equality-constrained optimization problems with only noisy function and derivative values. It is shown that the new interior-point algorithm drives a stationarity measure below a threshold that depends on bounds on the noise in the function and derivative values. The results of numerical experiments show that the algorithm is effective across a wide range of problems.

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arXiv2024

On the Convergence of Interior-Point Methods for Bound-Constrained Nonlinear Optimization Problems with Noise

We analyze the convergence properties of a modified barrier method for solving bound-constrained optimization problems where evaluations of the objective function and its derivatives are affected by bounded and non-diminishing noise. The only modification compared to a standard barrier method is a relaxation of the Armijo line-search condition. We prove that the algorithm generates iterates at which the size of the barrier function gradient eventually falls below a threshold that converges to zero if the noise level converges to zero. Based on this result, we propose a practical stopping test that does not require estimates of unknown problem parameters and identifies iterations in which the theoretical threshold is reached. We also analyze the local convergence properties of the method when noisy second derivatives are used. Under a strict-complementarity assumption, we show that iterates stay in a neighborhood around the optimal solution once it is entered. The neighborhood is defined in a scaled norm that becomes narrower for variables with active bound constraints as the barrier parameter is decreased. As a consequence, we show that active bound constraints can be identified despite noise. Numerical results demonstrate the effectiveness of the stopping test and illustrate the active-set identification properties of the method.

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arXiv2024

Derivative-Free Bound-Constrained Optimization for Solving Structured Problems with Surrogate Models

We propose and analyze a model-based derivative-free (DFO) algorithm for solving bound-constrained optimization problems where the objective function is the composition of a smooth function and a vector of black-box functions. We assume that the black-box functions are smooth and the evaluation of them is the computational bottleneck of the algorithm. The distinguishing feature of our algorithm is the use of approximate function values at interpolation points which can be obtained by an application-specific surrogate model that is cheap to evaluate. As an example, we consider the situation in which a sequence of related optimization problems is solved and present a regression-based approximation scheme that uses function values that were evaluated when solving prior problem instances. In addition, we propose and analyze a new algorithm for obtaining interpolation points that handles unrelaxable bound constraints. Our numerical results show that our algorithm outperforms a state-of-the-art DFO algorithm for solving a least-squares problem from a chemical engineering application when a history of black-box function evaluations is available.

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