Convex programs with an additional reverse convex constraint
Journal of Optimization Theory and Applications
Monotonic Optimization: Problems and Solution Approaches
SIAM Journal on Optimization
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
Optimization of Polynomial Fractional Functions
Journal of Global Optimization
Robust Solution of Nonconvex Global Optimization Problems
Journal of Global Optimization
Discrete Monotonic Optimization with Application to a Discrete Location Problem
SIAM Journal on Optimization
A robust algorithm for quadratic optimization under quadratic constraints
Journal of Global Optimization
A new topological minimax theorem with application
Journal of Global Optimization
Problems with resource allocation constraints and optimization over the efficient set
Journal of Global Optimization
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For solving global optimization problems with nonconvex feasible sets existing methods compute an approximate optimal solution which is not guaranteed to be close, within a given tolerance, to the actual optimal solution, nor even to be feasible. To overcome these limitations, a robust solution approach is proposed that can be applied to a wide class of problems called $${{\mathcal {D}(\mathcal {C})}}$$ -optimization problems. DC optimization and monotonic optimization are particular cases of $${{\mathcal {D}(\mathcal {C})}}$$ -optimization, so this class includes virtually every nonconvex global optimization problem of interest. The approach is a refinement and extension of an earlier version proposed for dc and monotonic optimization.