Chance-constrained optimization for nonconvex programs using scenario-based methods.

Area of Science:

• Optimization Theory
• Computational Mathematics

Background:

• Nonconvex programs with chance constraints present significant computational challenges.
• Existing methods often struggle with probabilistic feasibility and computational time.

Purpose of the Study:

• To develop an efficient scenario-based method for solving nonconvex chance-constrained optimization problems.
• To guarantee probabilistic feasibility and reduce solution conservatism in optimization.

Main Methods:

• A scenario-based method is proposed, generating deterministic approximations from sampled uncertain parameters.
• Sample complexity is analyzed to ensure probabilistic feasibility.
• A sequential approach and novel branching-and-sampling/discarding schemes are introduced for efficient global optimum seeking.

Main Results:

• The method effectively approximates chance-constrained nonconvex programs using large-scale deterministic models.
• The sequential approach and novel schemes accelerate the search for global optima.
• Effectiveness is demonstrated through applications in model predictive control and process scheduling.

Conclusions:

• The proposed scenario-based method offers an efficient and effective solution for nonconvex chance-constrained optimization.
• Novel schemes provide less conservative solutions for chance-constrained 0-1 programs.
• The approach is validated by successful applications in complex engineering problems.