On a subproblem of trust region algorithms for constrained optimization
Mathematical Programming: Series A and B
Hidden convexity in some nonconvex quadratically constrained quadratic programming
Mathematical Programming: Series A and B
Determinant Maximization with Linear Matrix Inequality Constraints
SIAM Journal on Matrix Analysis and Applications
Convexity of quadratic transformations and its use in control and optimization
Journal of Optimization Theory and Applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
Solution Methodologies for the Smallest Enclosing Circle Problem
Computational Optimization and Applications
New Results on Quadratic Minimization
SIAM Journal on Optimization
Efficient Algorithms for the Smallest Enclosing Ball Problem
Computational Optimization and Applications
Strong Duality in Nonconvex Quadratic Optimization with Two Quadratic Constraints
SIAM Journal on Optimization
SIAM Journal on Optimization
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We consider the outer approximation problem of finding a minimum radius ball enclosing a given intersection of at most n 驴 1 balls in $${\mathbb{R}^n}$$ . We show that if the aforementioned intersection has a nonempty interior, then the problem reduces to minimizing a convex quadratic function over the unit simplex. This result is established by using convexity and representation theorems for a class of quadratic mappings. As a byproduct of our analysis, we show that a class of nonconvex quadratic problems admits a tight semidefinite relaxation.