Nondifferentiable Multiplier Rules for Optimization and Bilevel Optimization Problems
From MaRDI portal
Publication:4652004
DOI10.1137/S1052623403424193zbMath1077.90077MaRDI QIDQ4652004
Publication date: 23 February 2005
Published in: SIAM Journal on Optimization (Search for Journal in Brave)
necessary optimality conditionssufficient optimality conditionsconstraint qualificationsbilevel optimization problemsMichel--Penot subdifferentialsNondifferentiable KKT necessary optimality conditions
Nonlinear programming (90C30) Hierarchical games (including Stackelberg games) (91A65) Optimality conditions and duality in mathematical programming (90C46) Nonsmooth analysis (49J52)
Related Items (38)
Asymptotic regularity for Lipschitzian nonlinear optimization problems with applications to complementarity constrained and bilevel programming ⋮ Generalized derivatives and nonsmooth optimization, a finite dimensional tour (with comments and rejoinder) ⋮ Existence of solution and algorithms for a class of bilevel variational inequalities with hierarchical nesting structure ⋮ Necessary conditions for efficiency in terms of the Michel–Penot subdifferentials ⋮ On bilevel programs with a convex lower-level problem violating Slater's constraint qualification ⋮ Constraint qualifications for nonsmooth mathematical programs with equilibrium constraints ⋮ Lagrange multipliers theorem and saddle point optimality criteria in mathematical programming ⋮ Optimality Conditions for Bilevel Programming: An Approach Through Variational Analysis ⋮ Generic Property of the Partial Calmness Condition for Bilevel Programming Problems ⋮ Optimality conditions for efficiency in locally Lipschitz vector equilibrium problem with constraints in terms of Michel-Penot's directional derivatives ⋮ Sufficient optimality conditions using convexifactors for optimistic bilevel programming problem ⋮ On optimality conditions and duality for multiobjective optimization with equilibrium constraints ⋮ Convergences for robust bilevel polynomial programmes with applications ⋮ Optimality Conditions Using Convexifactors for a Multiobjective Fractional Bilevel Programming Problem ⋮ Optimality conditions for optimistic bilevel programming problem using convexifactors ⋮ Variational analysis of marginal functions with applications to bilevel programming ⋮ Space splitting convexification: a local solution method for nonconvex optimal control problems ⋮ Optimization and flow invariance via first and second order tangent cones ⋮ The generalized Mangasarian-Fromowitz constraint qualification and optimality conditions for bilevel programs ⋮ The bilevel programming problem: reformulations, constraint qualifications and optimality conditions ⋮ Scalarization in geometric and functional vector optimization revisited ⋮ On nonsmooth V-invexity and vector variational-like inequalities in terms of the Michel-Penot subdifferentials ⋮ Boundedness of certain sets of Lagrange multipliers in vector optimization ⋮ On the Mangasarian-Fromovitz constraint qualification and Karush-Kuhn-Tucker conditions in nonsmooth semi-infinite multiobjective programming ⋮ ϵ-Efficient solutions in semi-infinite multiobjective optimization ⋮ A multiplier rule on a metric space ⋮ Quasiconvex minimization on a locally finite union of convex sets ⋮ Multiobjective DC programs with infinite convex constraints ⋮ New necessary optimality conditions in optimistic bilevel programming ⋮ Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints ⋮ Optimality conditions for bilevel programming problems ⋮ Optimality conditions for vector optimization problems ⋮ Stability for semivectorial bilevel programs ⋮ Quasiconvex programming with locally starshaped constraint region and applications to quasiconvex MPEC ⋮ Constraint Qualifications and Optimality Conditions in Bilevel Optimization ⋮ Bilevel Optimization: Theory, Algorithms, Applications and a Bibliography ⋮ Optimality Conditions and Duality for Semi-Infinite Mathematical Programming Problem with Equilibrium Constraints ⋮ Sufficient Optimality Conditions in Bilevel Programming
This page was built for publication: Nondifferentiable Multiplier Rules for Optimization and Bilevel Optimization Problems