Exact Augmented Lagrangian Duality for Mixed Integer Quadratic Programming

DOI10.1137/19M1271695OpenAlexW3010376936MaRDI QIDQ5853719

Xiaoyi Gu, Shabbir Ahmed, Santanu S. Dey

Publication date: 11 March 2021

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.00920

zbMATH Keywords

augmented Lagrangianinteger quadratic programmingstrong dual

Mathematics Subject Classification ID

Mixed integer programming (90C11) Quadratic programming (90C20) Optimality conditions and duality in mathematical programming (90C46)

Related Items

Special issue: Global solution of integer, stochastic and nonconvex optimization problems ⋮ Revisiting augmented Lagrangian duals

Cites Work

• Unnamed Item
• Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
• Some properties of convex hulls of integer points contained in general convex sets
• Exact augmented Lagrangian duality for mixed integer linear programming
• Mixed-integer quadratic programming is in NP
• Duality and exact penalization for general augmented Lagrangians
• Existence of augmented Lagrange multipliers for semi-infinite programming problems
• Quadratic programming is in NP
• An Exact Penalization Viewpoint of Constrained Optimization
• Bounds on Positive Integral Solutions of Linear Diophantine Equations
• On the existence of optimal solutions to integer and mixed-integer programming problems
• A Bound on Solutions of Linear Integer Equalities and Inequalities
• Variational Analysis
• A Strong Dual for Conic Mixed-Integer Programs
• A simple effective heuristic for embedded mixed-integer quadratic programming
• On Subadditive Duality for Conic Mixed-integer Programs
• Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming
• The Zero Duality Gap Property and Lower Semicontinuity of the Perturbation Function
• A Unified Augmented Lagrangian Approach to Duality and Exact Penalization