Generic nondegeneracy in convex optimization

Generic nondegeneracy in convex optimization

We show that minimizers of convex functions subject to almost all linear perturbations are nondegenerate. An analogous result holds more generally, for lower-C2 functions.

Generic identifiability and second-order sufficiency in tame convex optimization

We consider linear optimization over a fixed compact convex feasible region that is semi-algebraic (or, more generally, “tame”). Generically, we prove that the optimal solution is unique and lies on a unique manifold, around which the feasible region is “partly smooth”, ensuring finite identification of the manifold by many optimization algorithms. Furthermore, second-order optimality condition...

Convex Optimization

In this paper we propose an alternative solution to rl-blodr 1' problems. This altemativeis based upon the idea of transforming the I' problem into an equivalent (in the sense of having the same solution) mixed ll/'Hm problem that can be solved using convex optimieation techniques. The proposed algorithm has the advantage of generating, at each step, an upper bound of the cost that converges un...

On the generic properties of convex optimization problems in conic form

We prove that strict complementarity, primal and dual nondegeneracy of optimal solutions of convex optimization problems in conic form are generic properties. In this paper, we say generic to mean that the set of data possessing the desired property (or properties) has the same Hausdorr measure as the set of data that does not. Our proof is elementary and it employs an important result due to L...

Fejér Monotonicity in Convex Optimization