Related papers: Optimality conditions for an exhausterable functio…
The problem of finding the minimizer of a sum of convex functions is central to the field of optimization. Thus, it is of interest to understand how that minimizer is related to the properties of the individual functions in the sum. In this…
In this note we provide a full conjugacy and subdifferential calculus for convex convex-composite functions in finite-dimensional space. Our approach, based on infimal convolution and cone-convexity, is straightforward and yields the…
For a family of weight functions invariant under a finite reflection group, the boundedness of a maximal function on the unit sphere is established and used to prove a multiplier theorem for the orthogonal expansions with respect to the…
This paper identifies necessary and sufficient conditions for the exactness of penalty functions in optimization problems whose constraint sets are not necessarily bounded. The case where the data of problems is locally Lipschitz,…
We propose finitely convergent methods for solving convex feasibility problems defined over a possibly infinite pool of constraints. Following other works in this area, we assume that the interior of the solution set is nonempty and that…
Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued $C^{1,1}$-maps are presented. A novel characterization of strongly convex sets in terms of…
Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Combinatorial optimisation is the practice of selecting the best constituent…
The concept of efficiency plays a prominent role in the formal solution of decision problems that involve incomparable alternatives. This paper develops necessary and sufficient conditions for the efficient points in a sum of sets of…
We apply the topology of convergence on compact sets to define unpredictable functions [5, 6]. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and…
We show that a class of Poincar\'e-Wirtinger inequalities on bounded convex sets can be obtained by means of the dynamical formulation of Optimal Transport. This is a consequence of a more general result valid for convex sets, possibly…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
This paper investigates a specific class of nonsmooth nonconvex optimization problems in the face of data uncertainty, namely, robust optimization problems, where the given objective function can be expressed as a difference of two…
Around a solution of an optimization problem, an "identifiable" subset of the feasible region is one containing all nearby solutions after small perturbations to the problem. A quest for only the most essential ingredients of sensitivity…
The Fourier transform is naturally defined for integrable functrions. Otherwise, it should be stipulated in which sense the Fourier transform is understood. We consider some class of radial and, generally saying, nonintegrable functions.…
A family of real functions {g_\alpha} defining a spectral regularization method with optimal qualification is considered. Sufficient condition on the family and on the optimal qualification guaranteeing the existence of saturation are…
We study the mixed-integer epigraph of a special class of convex functions with non-convex indicator constraints, which are often used to impose logical constraints on the support of the solutions. The class of functions we consider are…
Shaping the reachable set of a dynamical system is a fundamental challenge in control design, with direct implications for both performance and safety. This paper considers the problem of selecting the optimal input matrix for a linear…
Approximate controllability of the Euler equations is investigated by means of a finite set of actuators. It is proven that approximate controllability holds if we can find a saturating subset of actuators. The notion of saturating set is…
An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…