# Fast, Dynamic, and Scalable Algorithms for Large-Scale Constrained Optimization

## Abstract

Scientists and engineers constantly aim to optimize an objective subject to physical, environmental, and/or resource constraints. The technique of using mathematical models to formulate and find real solutions of such problems is known as mathematical optimization, a process that has become invaluable for design and discovery in numerous scientific fields. This project has focused on the design, analysis, and implementation of high-performance computing algorithms for solving cutting-edge optimization problems. These include problems that involve (1) data uncertainties, such as those in the future supply, demand, and capacity of a given power system, (2) extreme numbers of alternatives, such as in the design of electrical power grids to avoid network vulnerabilities, and (3) real-time decisions, such as in the control of chemical reactors. The key features of the new algorithms are that they are fast, dynamic, and scalable to meet the computational requirements of scientists and researchers working to optimize large-scale, complex systems. The algorithms that have been designed, analyzed, and tested as part of the project can be characterized based on the types of optimization problems they have been designed to solve. Much of the work has focused on algorithms for solving large-scale constrained optimization problems. Contributions have also beenmore »

- Authors:

- Publication Date:

- Research Org.:
- Lehigh Univ., Bethlehem, PA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

- OSTI Identifier:
- 1569561

- Report Number(s):
- DOE-LEHIGH-10615

- DOE Contract Number:
- SC0010615

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Curtis, Frank Edward.
```*Fast, Dynamic, and Scalable Algorithms for Large-Scale Constrained Optimization*. United States: N. p., 2019.
Web. doi:10.2172/1569561.

```
Curtis, Frank Edward.
```*Fast, Dynamic, and Scalable Algorithms for Large-Scale Constrained Optimization*. United States. doi:10.2172/1569561.

```
Curtis, Frank Edward. Tue .
"Fast, Dynamic, and Scalable Algorithms for Large-Scale Constrained Optimization". United States. doi:10.2172/1569561. https://www.osti.gov/servlets/purl/1569561.
```

```
@article{osti_1569561,
```

title = {Fast, Dynamic, and Scalable Algorithms for Large-Scale Constrained Optimization},

author = {Curtis, Frank Edward},

abstractNote = {Scientists and engineers constantly aim to optimize an objective subject to physical, environmental, and/or resource constraints. The technique of using mathematical models to formulate and find real solutions of such problems is known as mathematical optimization, a process that has become invaluable for design and discovery in numerous scientific fields. This project has focused on the design, analysis, and implementation of high-performance computing algorithms for solving cutting-edge optimization problems. These include problems that involve (1) data uncertainties, such as those in the future supply, demand, and capacity of a given power system, (2) extreme numbers of alternatives, such as in the design of electrical power grids to avoid network vulnerabilities, and (3) real-time decisions, such as in the control of chemical reactors. The key features of the new algorithms are that they are fast, dynamic, and scalable to meet the computational requirements of scientists and researchers working to optimize large-scale, complex systems. The algorithms that have been designed, analyzed, and tested as part of the project can be characterized based on the types of optimization problems they have been designed to solve. Much of the work has focused on algorithms for solving large-scale constrained optimization problems. Contributions have also been made in the design of algorithms for unconstrained optimization, with some specialized methods for solving problems that have inherent nonsmoothness. Contributions have also been made in areas that have grown to prominence in the field over the five-year award period. These include the design of algorithms for solving large-scale stochastic optimization problems, such as those that arise in large-scale machine learning, and in complexity analyses for solving nonconvex problems, which has been a focal point of much recent work in continuous optimization. Overall, the project has supported work that has led to almost 30 articles that have been published or accepted to top journals in the field of mathematical optimization.},

doi = {10.2172/1569561},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2019},

month = {10}

}