How to deal with the unbounded in optimization: theory and algorithms
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
A Frank–Wolfe Type Theorem for Convex Polynomial Programs
Computational Optimization and Applications
On Generalizations of the Frank-Wolfe Theorem to Convex and Quasi-Convex Programmes
Computational Optimization and Applications
Global optimization of truss topology with discrete bar areas--Part I: theory of relaxed problems
Computational Optimization and Applications
A Conic Duality Frank--Wolfe-Type Theorem via Exact Penalization in Quadratic Optimization
Mathematics of Operations Research
Adaptive detection and estimation in the presence of useful signal and interference mismatches
IEEE Transactions on Signal Processing
Combining DC-programming and steepest-descent to solve the single-vehicle inventory routing problem
Computers and Industrial Engineering
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In this paper we consider optimization problems defined by aquadratic objective functionand a finite number of quadratic inequality constraints.Given that the objective function is bounded over the feasibleset, we present a comprehensive study of theconditions under which the optimal solution set is nonempty, thusextending the so-called Frank-Wolfe theorem.In particular, we first prove a general continuityresult for the solution set defined by a system ofconvex quadratic inequalities. This result implies immediatelythat the optimal solution set of the aforementioned problem isnonempty when all the quadratic functions involved are convex. In the absence of the convexity of the objective function,we give examples showing that the optimal solution set maybe empty either when there are two or more convex quadraticconstraints, or when the Hessian of the objective function has two or more negative eigenvalues. In the case when there exists only one convexquadratic inequality constraint (together with other linearconstraints), or when the constraintfunctions are all convex quadratic and the objective function isquasi-convex (thus allowing one negative eigenvalue in its Hessian matrix), we prove that the optimal solution set is nonempty.