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
Error bounds in mathematical programming
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
On Extensions of the Frank-Wolfe Theorems
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Remarks on the Analytic Centers of Convex Sets
Computational Optimization and Applications
On Generalizations of the Frank-Wolfe Theorem to Convex and Quasi-Convex Programmes
Computational Optimization and Applications
A Conic Duality Frank--Wolfe-Type Theorem via Exact Penalization in Quadratic Optimization
Mathematics of Operations Research
On the Asymptotically Well Behaved Functions and Global Error Bound for Convex Polynomials
SIAM Journal on Optimization
Minimum recession-compatible subsets of closed convex sets
Journal of Global Optimization
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In 1956, Frank and Wolfe extended the fundamental existence theorem of linear programming by proving that an arbitrary quadratic function f attains its minimum over a nonempty convex polyhedral set X provided f is bounded from below over X. We show that a similar statement holds if f is a convex polynomial and X is the solution set of a system of convex polynomial inequalities. In fact, this result was published by the first author already in a 1977 book, but seems to have been unnoticed until now. Further, we discuss the behavior of convex polynomial sets under linear transformations and derive some consequences of the Frank–Wolfe type theorem for perturbed problems.