Differentiability with respect to parameters of solutions to convex programming problems

DOI10.1007/BF01584382zbMath0582.49015MaRDI QIDQ3704503

Kazimierz Malanowski

Publication date: 1985

Published in: Mathematical Programming (Search for Journal in Brave)

zbMATH Keywords

metric projectionparametric convex programmingGateaux differentiabilityClarke's generalized derivative

Mathematics Subject Classification ID

Convex programming (90C25) Sensitivity, stability, parametric optimization (90C31) Fréchet and Gateaux differentiability in optimization (49J50) Continuity and differentiation questions (26B05)

Related Items (14)

Directional differentiability of optimal solutions under Slater's condition ⋮ The generalized jacobian of the optimal solution in parametric optimization ⋮ Sensitivity analysis in multiobjective optimization ⋮ Unnamed Item ⋮ A direct application of higher‐order parametric programming techniques to structural optimization ⋮ Directional differentiability of metric projections onto moving sets at boundary points ⋮ On the numerical solution of a class of Stackelberg problems ⋮ Directional differentiability of the metric projection operator in uniformly convex and uniformly smooth Banach spaces ⋮ Quasidifferntiability of optimal solutions in parametric optimal solutions in parametric nonlinear optimization ⋮ On the directional derivative of the optimal solution mapping without linear independence constraint qualification ⋮ The marginal value formula on regions of stability ⋮ Hölder behavior of optimal solutions and directional differentiability of marginal functions in nonlinear programming ⋮ Bundle trust-region algorithm for bilinear bilevel programming ⋮ Necessary optimality conditions for Stackelberg problems

Cites Work

• On the inverse function theorem
• Solution point differentiability without strict complementarity in nonlinear programming
• Lipschitz Continuity for Constrained Processes
• Strongly Regular Generalized Equations
• Sensitivity analysis for nonlinear programming using penalty methods
• Trajectory analysis and extrapolation in barrier function methods
• At What Points is the Projection Mapping Differentiable?
• Differentiability of the Metric Projection in Hilbert Space

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