This invention outlines a method to reformulate a convex semi-infinite optimization problem to an equivalent, finite-dimensional problem with finite constraints. This reformulation leads to a global maximization problem whose optimal value is equal to the optimal value of the original problem. This gives us an exact solution for semi-infinite optimization problems. The reformulation is done using
Figure (1) Block diagram of the electronic device architecture for global optimization of convex SIPs; (2) Flow diagram showing the working of the sampler device for reformulating SIP problems; (3) Flow chart of the sampling procedure with simulated annealing for convex SIPs; (4A) Histogram showing frequency of optimal value visits during optimization; (4B) Time evolution graph of the optimal value convergence over iterations; (5A) Plot showing absolute error vs iterations; (5B) Plot showing absolute error vs number of samples in optimization; (6) End-to-end flow diagram of the optimization problem solving steps via the sampler device.
Semi-infinite optimization problems are frequent in engineering, finance and machine learning problems. These problems aim to minimize the objective function of finite variables with possibly infinitely many constraints. Due to the uncountably many constraints, it becomes notoriously hard to compute an exact optimal value. Thus, a method is needed to exactly solve such problems with finite memory space.
- Compatibility with any global optimization algorithm: The method is a plug-n- play module that can work with any tailor-made deterministic or randomized global optimization algorithm
- Constant memory requirement: The method’s memory requirement depends only on the dimension of the optimized variables
- Independence of choice of optimization algorithm: The convexity of the constraint index has no role in the selection of the optimization algorithm that is used
The prototype comprises an electronic device architecture with core elements including a processor, memory, communicator, and a sampler device. It uses a simulated annealing–based global optimization technique to reformulate convex SIP problems into finite-dimensional, tractable forms. The prototype has been designed to handle inputs of problem-specific data (objective and constraint definitions) and output the exact optimal values of SIPs. Testing was performed in simulated conditions with benchmark problems, verifying the correct convergence to optimal solutions while maintaining a constant memory footprint regardless of the size of the constraint index set.
The technology has been developed up to the proof-of- concept stage, and a device architecture has been proposed for hardware implementation. The basic framework was validated for a range of convex semi-infinite programming (SIP) problems using a benchmark test database known as SIPAMPL. The implementation was carried out through a Python-based software with a plug-and-play module compatible with different global optimization techniques. The coded framework was tested with a simulated annealing routine at its core, and this implementation resulted in the recovery of exact optimal values that matched the theoretical values provided in the benchmark database.
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This innovation holds the potential to make a significant impact across sectors where high-dimensional constrained optimization is critical, such as robotics path planning, financial portfolio optimization, structural design, and aerospace controls. By ensuring exact solutions to convex semi-infinite problems with guaranteed convergence and bounded memory, the technology can enable safer, more efficient, and fairer optimization- based decisions. Ultimately, it supports better engineering systems, robust financial management, and enhanced safety and performance in automated and intelligent systems, contributing to a more optimized and reliable society.
- Robust Optimization: Solving high-dimensional optimization problems under uncertainty with guaranteed exact solutions.
- Portfolio Management: Improving risk-aware asset allocation with finite-memory exact optimization.
- Robotics Trajectory Planning: Providing safe and exact control of robots with infinitely constrained environments.
- Communication Systems: Designing protocols with robust performance guarantees under large sets of variable constraints.
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202121061723
512296