Outer approximation for convex MINLPs can cycle due to CQ failures or approximate solves, but extended cutting planes ensure finite convergence under weaker constraint qualification assumptions.
Necessary optimality condi- tions in pessimistic bilevel programming
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Pessimistic linear bilevel optimization problems with coupling constraints are equivalent to pessimistic and optimistic versions without them.
Derives second-order Dini formulas for efficient solution maps S from marginal maps Φ under value-to-decision error bounds and metric regularity conditions in parametric vector optimization.
A variable-metric non-monotone line search method based on the Fukushima regularized gap function is introduced for mixed variational inequalities and equilibrium problems, with global convergence and R-linear rate proved under strong monotonicity.
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Separation, Constraint Qualifications, and Cycling in Outer Approximation
Outer approximation for convex MINLPs can cycle due to CQ failures or approximate solves, but extended cutting planes ensure finite convergence under weaker constraint qualification assumptions.
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Second-Order Sensitivity of Efficient Solution and Marginal Maps in Parametric Vector Optimization with Set Constraints
Derives second-order Dini formulas for efficient solution maps S from marginal maps Φ under value-to-decision error bounds and metric regularity conditions in parametric vector optimization.
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A Variable-Metric Non-monotone Line Search Method for Mixed Variational Inequalities and Equilibrium Problems
A variable-metric non-monotone line search method based on the Fukushima regularized gap function is introduced for mixed variational inequalities and equilibrium problems, with global convergence and R-linear rate proved under strong monotonicity.