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Mathematical and Resource Optimization

The Mathematical and Resource Optimization program supports basic research in optimization — focusing on the development of theory and algorithms for large-scale optimization problems. Application-driven research in optimization is supported by the Resource Optimization thrust under the Computational Methods for Decision Making program.

The primary focus of the Mathematical Optimization program is the development of new, cutting-edge theory and algorithms for efficiently solving problems in linear, nonlinear, integer, and combinatorial optimization. Areas of interest include:

  • Theoretical development
  • Algorithmic design and analysis
  • Computational methods
  • Software prototypes for large-scale problems

This directive includes, but is not limited to:

  • Cutting plane and polyhedral techniques for mixed-integer programming
  • Decomposition approaches for large (non)convex problems
  • Interior-point and first-order algorithms for conic/convex optimization

Advances that produce provably optimal or near-optimal solutions, as well as those applicable to large problem domains, are favored. Innovative strategies for dealing with uncertainty from stochastic optimization, robust optimization, and simulation-based optimization are of growing interest. Research supported by this program is expected to make fundamental contributions to the field of mathematical optimization.

Research Concentration Areas

Problems in Mathematical Optimization arise in a variety of Navy scenarios, including interdiction, logistics, planning, scheduling, and sequencing.

These problems, which can be continuous and/or discrete, require theoretical and algorithmic advances in such areas as:

  • Conic programming
  • Large-scale linear programming
  • Mixed-integer programming
  • Multi-level optimization
  • Nonlinear programming

The efforts funded under this program are basic research so that, while direct linkages to Navy problems are not required, potential for future applicability should exist.

Research Challenges and Opportunities

  • Develop new theory for efficiently solving mathematical optimization problems.
  • Devise provably-optimal solution algorithms that advance state-of-the-art methods.
  • Identify and exploit mathematical structures to most efficiently optimize important families of problems.

How to Submit

For detailed application and submission information for this research topic, please refer to our broad agency announcement (BAA) No. N00014-23-S-B001.

Contracts: All white papers and full proposals for contracts must be submitted through FedConnect; instructions are included in the BAA.

Grants: All white papers for grants must be submitted through FedConnect, and full proposals for grants must be submitted through; instructions are included in the BAA.


Phillips, David J. Dr.
Program Officer
Code 311