A globally convergent SQP method for semi-infinite nonlinear optimization
Journal of Computational and Applied Mathematics
A computational algorithm for functional inequality constrained optimization problems
Automatica (Journal of IFAC)
Numerical experiments in semi-infinite programming
Computational Optimization and Applications
Optimization: algorithms and consistent approximations
Optimization: algorithms and consistent approximations
An accelerated central cutting plane algorithm for linear semi-infinite programming
Mathematical Programming: Series A and B
Interval methods for semi-infinite programs
Computational Optimization and Applications
Global solution of semi-infinite programs
Mathematical Programming: Series A and B
A Truncated Projected Newton-Type Algorithm for Large-Scale Semi-infinite Programming
SIAM Journal on Optimization
Deterministic Global Optimization: Theory, Methods and (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 37) (Nonconvex Optimization and Its Applications)
The Adaptive Convexification Algorithm: A Feasible Point Method for Semi-Infinite Programming
SIAM Journal on Optimization
A smoothing projected Newton-type algorithm for semi-infinite programming
Computational Optimization and Applications
A New Exchange Method for Convex Semi-Infinite Programming
SIAM Journal on Optimization
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In this paper, we present an algorithm to solve nonlinear semi-infinite programming (NSIP) problems. To deal with the nonlinear constraint, Floudas and Stein (SIAM J. Optim. 18:1187---1208, 2007) suggest an adaptive convexification relaxation to approximate the nonlinear constraint function. The 驴BB method, used widely in global optimization, is applied to construct the convexification relaxation. We then combine the idea of the cutting plane method with the convexification relaxation to propose a new algorithm to solve NSIP problems. With some given tolerances, our algorithm terminates in a finite number of iterations and obtains an approximate stationary point of the NSIP problems. In addition, some NSIP application examples are implemented by the method proposed in this paper, such as the proportional-integral-derivative controller design problem and the nonlinear finite impulse response filter design problem. Based on our numerical experience, we demonstrate that our algorithm enhances the computational speed for solving NSIP problems.