Domain-specific languages for convex and non-convex optimization
Abstract/Contents
- Abstract
- Convex optimization has many applications to fields as diverse as machine learning, control, finance, and signal and image processing. Using convex optimization in an application requires either developing a custom solver or converting the problem into a standard form. Both of these tasks require expertise, and are time-consuming and error prone. An alternative is to use a domain-specific language (DSL) for convex optimization, which allows the user to specify the problem in a natural way that follows the math; this specification is then automatically converted into the standard form required by generic solvers. In this thesis we demonstrate that DSLs for convex optimization are easy to use, scale to large problems, and can be extended to useful classes of non-convex problems. We begin with a discussion of CVXPY, a widely-used DSL for convex optimization. We present several examples of modeling optimization problems with CVXPY and highlight the novel features and modeling paradigms CVXPY introduced. We next illustrate how DSLs for convex optimization such as CVXPY can be extended to efficiently handle large-scale optimization problems involving structured linear operators. We call our approach matrix-free convex optimization modeling. We conclude with an exploration of non-convex optimization using convex optimization as a black-box method. In particular, we consider approximate minimization of convex functions over non-convex sets via an ADMM-based heuristic that solves a series of convex subproblems. Our approach lends itself to expression as a DSL, which we call NCVX
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2020; ©2020 |
| Publication date | 2020; 2020 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Diamond, Steven Malone |
|---|---|
| Degree supervisor | Boyd, Stephen P |
| Degree supervisor | Ré, Christopher |
| Thesis advisor | Boyd, Stephen P |
| Thesis advisor | Ré, Christopher |
| Thesis advisor | Aiken, Alexander |
| Thesis advisor | Wetzstein, Gordon |
| Degree committee member | Aiken, Alexander |
| Degree committee member | Wetzstein, Gordon |
| Associated with | Stanford University, Computer Science Department. |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Steven Malone Diamond |
|---|---|
| Note | Submitted to the Computer Science Department |
| Thesis | Thesis Ph.D. Stanford University 2020 |
| Location | electronic resource |
Access conditions
- Copyright
- © 2020 by Steven Malone Diamond
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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