EUROPT 2024
Abstract Submission

320. Pushing the limits of interior methods for nonlinear optimization

Invited abstract in session TC-2: Developments in interior point methods, stream Developments in interior point methods.

Thursday, 11:25 - 12:40
Room: M:O

Authors (first author is the speaker)

1. Anders Forsgren
Department of Mathematics, KTH Royal Institute of Technology
2. Pim Heeman
Department of Mathematics, KTH Royal Institute of Technology

Abstract

Interior methods form a powerful class of methods for solving nonlinear optimization problems. The main computational work lies in solving the linear equations that arise when Newton's method is applied to solving a set of nonlinear equations. The nonlinear equations may be of primal form, setting the gradient of the log barrier function to zero, or of primal-dual form, formulated as a perturbation of the first-order necessary optimality conditions.

The ability to solve large problems is therefore tied to the ability to solve the large systems of linear equations. An important feature is that the optimal solution to the optimization problem is what is desired, neither the optimal solution to a nonlinear equation for a given value of the barrier parameter nor the solution to the particular linear system of equations. There will be a tradeoff between the accuracy in the solution of the linear equations and the overall computational cost for solving the optimization problem.

In the talk, past and ongoing work in this area, in which the speaker has been involved, will be discussed.

Keywords

Status: accepted


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