On an algorithm solving two-level programming problems with nonunique lower level solutions

DOI10.1007/BF00247793zbMath0858.90116MaRDI QIDQ1814990

H. Schmidt, Stephan Dempe

Publication date: 3 November 1996

Published in: Computational Optimization and Applications (Search for Journal in Brave)

zbMATH Keywords

convergence prooftwo-level programmingstepsizedirection of descent

Mathematics Subject Classification ID

Nonlinear programming (90C30) Sensitivity, stability, parametric optimization (90C31)

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Cites Work

• Unnamed Item
• Unnamed Item
• Introduction to sensitivity and stability analysis in nonlinear programming
• Geometric and algorithmic developments for a hierarchical planning problem
• Existence of optimal solutions to mathematical programs with equilibrium constraints
• Convex two-level optimization
• Double penalty method for bilevel optimization problems
• Bilevel and multilevel programming: A bibliography review
• Directional differentiability of optimal solutions under Slater's condition
• Solution point differentiability without strict complementarity in nonlinear programming
• Network design problem with congestion effects: A case of bilevel programming
• Local structure of feasible sets in nonlinear programming, Part III: Stability and sensitivity
• Existence theorems of equilibrium points in stackelberg
• Sensitivity Analysis of Nonlinear Programs and Differentiability Properties of Metric Projections
• On some recent engineering applications of complementarity problems
• Minimization of Locally Lipschitzian Functions
• A necessary and sufficient regularity condition to have bounded multipliers in nonconvex programming
• A necessary and a sufficient optimality condition for bilevel programming problems
• Directional Derivatives for Extremal-Value Functions with Applications to the Completely Convex Case

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