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Inexact and Stochastic Large-Scale N...

Wang, Qi,

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Inexact and Stochastic Large-Scale Nonlinear Optimization /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Inexact and Stochastic Large-Scale Nonlinear Optimization // Qi Wang.
作者:	Wang, Qi,
面頁冊數:	1 electronic resource (231 pages)
附註:	Source: Dissertations Abstracts International, Volume: 86-07, Section: B.
Contained By:	Dissertations Abstracts International86-07B.
標題:	Industrial engineering. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31762099
ISBN:	9798302180308

Inexact and Stochastic Large-Scale Nonlinear Optimization /
Wang, Qi,

Inexact and Stochastic Large-Scale Nonlinear Optimization /Qi Wang. - 1 electronic resource (231 pages)

Source: Dissertations Abstracts International, Volume: 86-07, Section: B.

Nonlinear optimization algorithms often use iterative methods. Typically, starting from an initial point, an algorithm computes a step, determines a step size, and updates the solution estimate using the step and step size. The type of iterative method that is employed should depend on the size of the problem, namely, whether it is small or large. In this thesis, we focus on methods for solving large-scale problems. An optimization problem can be large in different responses; for example, the number of variables may be large and/or a dataset that defines the problem functions may be large. This latter type is common in areas such as machine learning. This thesis addresses nonlinear optimization algorithm design for solving large-scale problems of both of the aforementioned types.First, we design a trust-region method for solving nonconvex unconstrained problems when the number of variables is large and solving the trust-region subproblem exactly is intractable. Another goal of the algorithm is to maintain the optimal worst-case complexity of O(ϵ −3/2 ) that is achieved by a trust-region method based on exact subproblem solutions. To achieve this, we propose some sufficient conditions that the inexact subproblem solutions must satisfy to maintain the optimal complexity, as well as a computationally efficient Krylov method for obtaining inexact solutions that satisfy these sufficient conditions.Second, when the dataset describing an optimization problem is large, evaluating the gradients, objective, etc., becomes expensive. This setting applies to optimization problems in machine learning, such as those minimizing expected risk and empirical risk. We address such settings that also involve nonlinear constraints on the design variables. Specifically, we consider cases where only minibatch (i.e., stochastic) gradient of the objective are accessible, but the constraint, and the constraint derivative are available. We design two groups of algorithms-Sequential Quadratic Programming (SQP) and Interior Point Methods (IPM)-both with guarantees to converge to a KKT solution under reasonable assumptions. We also apply our SQP method to solve physics-informed machine learning problems, demonstrating improved performance over unconstrained approaches, such as penalty methods.

English

ISBN: 9798302180308Subjects--Topical Terms:

526216
Industrial engineering.
Subjects--Index Terms:

Constrained optimization

Inexact and Stochastic Large-Scale Nonlinear Optimization /
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500 $a Source: Dissertations Abstracts International, Volume: 86-07, Section: B.
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520 $a Nonlinear optimization algorithms often use iterative methods. Typically, starting from an initial point, an algorithm computes a step, determines a step size, and updates the solution estimate using the step and step size. The type of iterative method that is employed should depend on the size of the problem, namely, whether it is small or large. In this thesis, we focus on methods for solving large-scale problems. An optimization problem can be large in different responses; for example, the number of variables may be large and/or a dataset that defines the problem functions may be large. This latter type is common in areas such as machine learning. This thesis addresses nonlinear optimization algorithm design for solving large-scale problems of both of the aforementioned types.First, we design a trust-region method for solving nonconvex unconstrained problems when the number of variables is large and solving the trust-region subproblem exactly is intractable. Another goal of the algorithm is to maintain the optimal worst-case complexity of O(ϵ −3/2 ) that is achieved by a trust-region method based on exact subproblem solutions. To achieve this, we propose some sufficient conditions that the inexact subproblem solutions must satisfy to maintain the optimal complexity, as well as a computationally efficient Krylov method for obtaining inexact solutions that satisfy these sufficient conditions.Second, when the dataset describing an optimization problem is large, evaluating the gradients, objective, etc., becomes expensive. This setting applies to optimization problems in machine learning, such as those minimizing expected risk and empirical risk. We address such settings that also involve nonlinear constraints on the design variables. Specifically, we consider cases where only minibatch (i.e., stochastic) gradient of the objective are accessible, but the constraint, and the constraint derivative are available. We design two groups of algorithms-Sequential Quadratic Programming (SQP) and Interior Point Methods (IPM)-both with guarantees to converge to a KKT solution under reasonable assumptions. We also apply our SQP method to solve physics-informed machine learning problems, demonstrating improved performance over unconstrained approaches, such as penalty methods.
546 $a English
590 $a School code: 0105
650 4 $a Industrial engineering. $3 526216
650 4 $a Engineering. $3 586835
650 4 $a Mechanical engineering. $3 649730
653 $a Constrained optimization
653 $a Continuous optimization
653 $a Interior Point Methods
653 $a Sequential Quadratic Programming
653 $a Stochastic optimization
653 $a Trust-region method
690 $a 0546
690 $a 0537
690 $a 0548
710 2 $a Lehigh University. $b Industrial Engineering. $e degree granting institution. $3 3770521
720 1 $a Curtis, Frank E. $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-07B.
790 $a 0105
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31762099