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DROP Optimization

DROP Optimization implements the Necessary, Sufficient, and Regularity Checks for Gradient Descent in a Constrained Optimization Setup as well LP/ILP/MINLP Schemes.

Component Packages

  • Canonical DROP Optimization Canonical Package implements Polyhedral Cutting Plane Generation Schemes.

  • Constrained DROP Optimization Constrained implements the KKT Fritz-John Constrained Optimizer Framework.

  • Cutting Plane DROP Optimization Cutting Plane Package implements Polyhedral Cutting Plane Generation Schemes.

  • Necessary DROP Optimization Necessary Package implements the Constrained Optimizer Necessary Sufficient Conditions.

  • Regularity DROP Optimization Regularity Package implements the Constrained Optimizer Regularity Qualifier Conditions.

References

  • Boyd, S., and L. van den Berghe (2009): Convex Optimization Cambridge University Press Cambridge UK

  • Burdet, C. A., and E. L. Johnson (1977): A Sub-additive Approach to Solve Linear Integer Programs Annals of Discrete Mathematics 1 117-143

  • Chvatal, V. (1973): Edmonds Polytopes in a Hierarchy of Combinatorial Problems Discrete Mathematics 4 (4) 305-337

  • Eustaquio, R., E. Karas, and A. Ribeiro (2008): Constraint Qualification for Nonlinear Programming Federal University of Parana

  • Gomory, R. E. (1958): Outline of an Algorithm for Integer Solutions to Linear Programs Bulletin of the American Mathematical Society 64 (5) 275-278

  • Karush, A. (1939): Minima of Functions of Several Variables with Inequalities as Side Constraints University of Chicago Chicago IL

  • Kelley, J. E. (1960): The Cutting Plane Method for Solving Convex Problems Journal for the Society of the Industrial and Applied Mathematics 8 (4) 703-712

  • Kuhn, H. W., and A. W. Tucker (1951): Nonlinear Programming Proceedings of the Second Berkeley Symposium University of California Berkeley CA 481-492

  • Letchford, A. N. and A. Lodi (2002): Strengthening Chvatal-Gomory Cuts and Gomory Fractional Cuts Operations Research Letters 30 (2) 74-82

  • Ruszczynski, A. (2006): Nonlinear Optimization Princeton University Press Princeton NJ

DROP Specifications