Regularity conditions via generalized interiority notions in convex optimization: New achievements and their relation to some classical statements

DOI10.1080/02331934.2010.505649zbMath1246.46062arXiv0906.0453OpenAlexW2593814001MaRDI QIDQ3225066

Radu Ioan Boţ, Ernö Robert Csetnek

Publication date: 15 March 2012

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.0453

zbMATH Keywords

convex optimizationperturbation theoryLagrange dualityFenchel dualityquasi-relative interiorquasi-interior

Mathematics Subject Classification ID

Convex programming (90C25) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10)

Related Items (23)

Fenchel–Rockafellar theorem in infinite dimensions via generalized relative interiors ⋮ Characterizations of improvement sets via quasi interior and applications in vector optimization ⋮ Inertial Douglas-Rachford splitting for monotone inclusion problems ⋮ Characterizations via linear scalarization of minimal and properly minimal elements ⋮ Revisiting the construction of gap functions for variational inequalities and equilibrium problems via conjugate duality ⋮ Refinements on gap functions and optimality conditions for vector quasi-equilibrium problems via image space analysis ⋮ Inertial viscosity iterative method for solving pseudo-monotone variational inequality problems and fixed point problems ⋮ Higher-order Karush-Kuhn-Tucker optimality conditions for set-valued optimization with nonsolid ordering cones ⋮ Convex and convex-like optimization over a range inclusion problem and first applications ⋮ On some erroneous statements in the paper ``Optimality conditions for extended Ky Fan inequality with cone and affine constraints and their applications by A. Capătă ⋮ Infinite-dimensional vector optimization and a separation theorem ⋮ Finitely convergent iterative methods with overrelaxations revisited ⋮ On epsilon-stability in optimization ⋮ Vector duality for convex vector optimization problems by means of the quasi-interior of the ordering cone ⋮ Unifying local-global type properties in vector optimization ⋮ Strong convergence theorems for solving variational inequality problems with pseudo-monotone and non-Lipschitz operators ⋮ On the use of the quasi-relative interior in optimization ⋮ On Lagrange Duality for Several Classes of Nonconvex Optimization Problems ⋮ On the convergence rate of a forward-backward type primal-dual splitting algorithm for convex optimization problems ⋮ Local maximum points of explicitly quasiconvex functions ⋮ A characterization of cone-convexity for set-valued functions by cone-quasiconvexity ⋮ Lagrange duality for evenly convex optimization problems ⋮ An inertial forward-backward-forward primal-dual splitting algorithm for solving monotone inclusion problems

Cites Work

• Necessary and sufficient conditions for \(S\)-lemma and~nonconvex quadratic optimization
• New dual constraint qualifications characterizing zero duality gaps of convex programs and semidefinite programs
• Stable zero duality gaps in convex programming: complete dual characterisations with applications to semidefinite programs
• Complete characterizations of stable Farkas' lemma and cone-convex programming duality
• Revisiting some duality theorems via the quasirelative interior in convex optimization
• Some convex programs without a duality gap
• Duality gap of the conic convex constrained optimization problems in normed spaces
• Extended monotropic programming and duality
• Semi-continuous mappings in general topology
• Partially finite convex programming. I: Quasi relative interiors and duality theory
• Generalizations of Slater's constraint qualification for infinite convex programs
• Quasi interiors, Lagrange multipliers, and \(L^ p\) spectral estimation with lattice bounds
• Generalized semicontinuity and existence theorems for cone saddle points
• Notions of relative interior in Banach spaces
• Separation theorem based on the quasirelative interior and application to duality theory
• The convexity of \(A\) and \(B\) assures \(\text{int} A + B = \text{int}(A + B)\)
• General infinite dimensional duality and applications to evolutionary network equilibrium problems
• On strong and total Lagrange duality for convex optimization problems
• Infinite dimensional duality and applications
• A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces.
• An alternative formulation for a new closed cone constraint qualification
• Necessary and sufficient conditions for stable conjugate duality
• Lower semicontinuous regularization for vector-valued mappings
• A new geometric condition for Fenchel's duality in infinite dimensional spaces
• A Comparison of Constraint Qualifications in Infinite-Dimensional Convex Programming
• The Fenchel duality theorem in Fréchet spaees
• Stable and Total Fenchel Duality for Convex Optimization Problems in Locally Convex Spaces
• Constraint Qualifications for Extended Farkas's Lemmas and Lagrangian Dualities in Convex Infinite Programming
• Constraint Qualifications for Convex Inequality Systems with Applications in Constrained Optimization
• Regularity Conditions via Quasi-Relative Interior in Convex Programming
• Fenchel and Lagrange duality are equivalent
• A comparison of constraint qualifications in infinite-dimensional convex programming revisited

This page was built for publication: Regularity conditions via generalized interiority notions in convex optimization: New achievements and their relation to some classical statements