On a subproblem of trust region algorithms for constrained optimization
Mathematical Programming: Series A and B
A trust region algorithm for equality constrained optimization
Mathematical Programming: Series A and B
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
On Local Solutions of the Celis--Dennis--Tapia Subproblem
SIAM Journal on Optimization
Optimality Conditions for the Minimization of a Quadratic with Two Quadratic Constraints
SIAM Journal on Optimization
A New Trust-Region Algorithm for Equality Constrained Optimization
Computational Optimization and Applications
New Results on Quadratic Minimization
SIAM Journal on Optimization
Convex Optimization
Seizure warning algorithm based on optimization and nonlinear dynamics
Mathematical Programming: Series A and B
Strong Duality in Nonconvex Quadratic Optimization with Two Quadratic Constraints
SIAM Journal on Optimization
Non-convex quadratic minimization problems with quadratic constraints: global optimality conditions
Mathematical Programming: Series A and B
Strong Duality for the CDT Subproblem: A Necessary and Sufficient Condition
SIAM Journal on Optimization
SIAM Review
Alternative Theorems for Quadratic Inequality Systems and Global Quadratic Optimization
SIAM Journal on Optimization
A new linearization technique for multi-quadratic 0-1 programming problems
Operations Research Letters
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In this paper we first establish a Lagrange multiplier condition characterizing a regularized Lagrangian duality for quadratic minimization problems with finitely many linear equality and quadratic inequality constraints, where the linear constraints are not relaxed in the regularized Lagrangian dual. In particular, in the case of a quadratic optimization problem with a single quadratic inequality constraint such as the linearly constrained trust-region problems, we show that the Slater constraint qualification (SCQ) is necessary and sufficient for the regularized Lagrangian duality in the sense that the regularized duality holds for each quadratic objective function over the constraints if and only if (SCQ) holds. A new theorem of the alternative for systems involving both equality constraints and two quadratic inequality constraints plays a key role. We also provide classes of quadratic programs, including a class of CDT-subproblems with linear equality constraints, where (SCQ) ensures regularized Lagrangian duality.