Necessary and sufficient conditions for \(S\)-lemma and~nonconvex quadratic optimization
From MaRDI portal
Publication:374638
DOI10.1007/s11081-008-9076-9zbMath1273.90141OpenAlexW2058387991WikidataQ59241577 ScholiaQ59241577MaRDI QIDQ374638
Guoyin Li, Nguyen Quang Huy, Vaithilingam Jeyakumar
Publication date: 24 October 2013
Published in: Optimization and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11081-008-9076-9
Slater's condition\(S\)-lemmanecessary and sufficient global optimality conditionsnonconvex quadratic optimizationregularized \(S\)-lemma
Related Items (21)
A tensor analogy of Yuan's theorem of the alternative and polynomial optimization with sign structure ⋮ Robust canonical duality theory for solving nonconvex programming problems under data uncertainty ⋮ Finding the maximum eigenvalue of essentially nonnegative symmetric tensors via sum of squares programming ⋮ Strong duality and KKT conditions in nonconvex optimization with a single equality constraint and geometric constraint ⋮ Regularity conditions via generalized interiority notions in convex optimization: New achievements and their relation to some classical statements ⋮ Regularized Lagrangian duality for linearly constrained quadratic optimization and trust-region problems ⋮ Global quadratic minimization over bivalent constraints: necessary and sufficient global optimality condition ⋮ Robust solutions of quadratic optimization over single quadratic constraint under interval uncertainty ⋮ Quadratically adjustable robust linear optimization with inexact data via generalized S-lemma: exact second-order cone program reformulations ⋮ A note on nonconvex minimax theorem with separable homogeneous polynomials ⋮ Exact Second-Order Cone Programming Relaxations for Some Nonconvex Minimax Quadratic Optimization Problems ⋮ Global optimality principles for polynomial optimization over box or bivalent constraints by separable polynomial approximations ⋮ A complete characterization of strong duality in nonconvex optimization with a single constraint ⋮ On weak conjugacy, augmented Lagrangians and duality in nonconvex optimization ⋮ Robust duality for generalized convex programming problems under data uncertainty ⋮ On stability of solutions to parametric generalized affine variational inequalities ⋮ Semidefinite program duals for separable polynomial programs involving box constraints ⋮ A geometric characterization of strong duality in nonconvex quadratic programming with linear and nonconvex quadratic constraints ⋮ A new class of alternative theorems for SOS-convex inequalities and robust optimization ⋮ On fractional quadratic optimization problem with two quadratic constraints ⋮ S-lemma with equality and its applications
Cites Work
- Unnamed Item
- Liberating the subgradient optimality conditions from constraint qualifications
- On the S-procedure and some variants
- Complete characterizations of stable Farkas' lemma and cone-convex programming duality
- Non-convex quadratic minimization problems with quadratic constraints: global optimality conditions
- Sequential Lagrangian conditions for convex programs with applications to semidefinite programming
- Convexity of quadratic transformations and its use in control and optimization
- The strong conical hull intersection property for convex programming
- A new geometric condition for Fenchel's duality in infinite dimensional spaces
- Lectures on Modern Convex Optimization
- On the Field of Values of a Matrix
- New Sequential Lagrange Multiplier Conditions Characterizing Optimality without Constraint Qualification for Convex Programs
- Multivariate Nonnegative Quadratic Mappings
- Nonlinear Extensions of Farkas’ Lemma with Applications to Global Optimization and Least Squares
- On Cones of Nonnegative Quadratic Functions
- A Survey of the S-Lemma
This page was built for publication: Necessary and sufficient conditions for \(S\)-lemma and~nonconvex quadratic optimization