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
A Frank–Wolfe Type Theorem for Convex Polynomial Programs
Computational Optimization and Applications
On the Minimizing Trajectory of Convex Functions with Unbounded Level Sets
Computational Optimization and Applications
Remarks on the Analytic Centers of Convex Sets
Computational Optimization and Applications
Minimal infeasible constraint sets in convex integer programs
Journal of Global Optimization
On the Asymptotically Well Behaved Functions and Global Error Bound for Convex Polynomials
SIAM Journal on Optimization
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In this paper we are concerned with the problem of boundedness and the existence of optimal solutions to the constrained optimization problem.We present necessary and sufficient conditions for boundedness of either a faithfully convex or a quasi-convex polynomial function over the feasible set defined by a system of faithfully convex inequality constraints and/or quasi-convex polynomial inequalities, where the faithfully convex functions satisfy some mild assumption. The conditions are provided in the form of an algorithm, terminating after a finite number of iterations, the implementation of which requires the identification of implicit equality constraints in a homogeneous linear system. We prove that the optimal solution set of the considered problem is nonempty, this way extending the attainability result well known as the so-called Frank-Wolfe theorem. Finally we show that our extension of the Frank-Wolfe theorem immediately implies continuity of the solution set defined by the considered system of (quasi)convex inequalities.