The Dynamics of Nonlinear Relaxation Labeling Processes
Journal of Mathematical Imaging and Vision
Trust region affine scaling algorithms for linearly constrained convex and concave programs
Mathematical Programming: Series A and B
On Extensions of the Frank-Wolfe Theorems
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
A Frank–Wolfe Type Theorem for Convex Polynomial Programs
Computational Optimization and Applications
Convex Optimization
Multi-Standard Quadratic Optimization: interior point methods and cone programming reformulation
Computational Optimization and Applications
Journal of Global Optimization
Standard bi-quadratic optimization problems and unconstrained polynomial reformulations
Journal of Global Optimization
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The famous Frank--Wolfe theorem ensures attainability of the optimal value for quadratic objective functions over a (possibly unbounded) polyhedron if the feasible values are bounded. This theorem does not hold in general for conic programs where linear constraints are replaced by more general convex constraints like positive semidefiniteness or copositivity conditions, despite the fact that the objective can be even linear. This paper studies exact penalizations of (classical) quadratic programs, i.e., optimization of quadratic functions over a polyhedron, and applies the results to establish a Frank--Wolfe-type theorem for the primal-dual pair of a class of conic programs that frequently arises in applications. One result is that uniqueness of the solution of the primal ensures dual attainability, i.e., existence of the solution of the dual.