We prove necessary optimality conditions of Euler–Lagrange type for generalized problems of the calculus of variations on time scales with a Lagrangian depending not only on the independent variable, an unknown function and its delta derivative, but also on a delta indefinite integral that depends on the unknown function. Such kind of variational problems were considered by Euler himself and ha...

Abstract. In this paper we continue our study, begun in [11], of the exceptional set of integers, not restricted by elementary congruence conditions, which cannot be represented as sums of three or four squares of primes. We correct a serious oversight in our first paper, but make further progress on the exponential sums estimates needed, together with an embellishment of the previous sieve tec...

The strong conical hull intersection property and bounded linear regularity are properties of a collection of finitely many closed convex intersecting sets in Euclidean space. These fundamental notions occur in various branches of convex optimization (constrained approximation, convex feasibility problems, linear inequalities, for instance). It is shown that the standard constraint qualificatio...

In this paper, we consider stochastic optimal control of Markov Jump Linear Systems with state feedback but without observation of the jumping parameter. The proposed control law is assumed to be linear with constant gains that can be obtained from the necessary optimality conditions using an iterative algorithm. The proposed approach is demonstrated in a numerical example.

Optimal control under state constraints has brought new mathematical challenges that have led to new techniques and new theories. We survey some recent results related to issues of regularity of optimal trajectories, optimal controls and the value function, and discuss optimal synthesis and necessary optimality conditions. We also show how abstract inverse mapping theorems of set-valued analysi...

This paper concerns a method for finding the minimum of a polynomial on a semialgebraic set, i.e., a set in R defined by finitely many polynomial equations and inequalities, using the Karush-Kuhn-Tucker (KKT) system and sum of squares (SOS) relaxations. This generalizes results in the recent paper [15], which considers minimizing polynomials on algebraic sets, i.e., sets in R defined by finitel...

We consider a stochastic control problem, where the control domain is convex and the system is governed by a nonlinear backward stochastic differential equation. With a L1 terminal data, we derive necessary optimality conditions in the form of stochastic maximum principle. AMS Subject Classification. 93Exx

Recent debate on the reform of the international financial architecture has highlighted the potentially important role of the official sector in crisis management. We examine how such public intervention in sovereign debt crises affects efficiency, ex ante and ex post. Our results shed light on the scale of capital inflows in such a regime, and we establish conditions under which this leads to ...

The theory of graph games with ω-regular winning conditions is the foundation for modeling and synthesizing reactive processes. In the case of stochastic reactive processes, the corresponding stochastic graph games have three players, two of them (System and Environment) behaving adversarially, and the third (Uncertainty) behaving probabilistically. We consider two problems for stochastic graph...

A standard quadratic optimization problem (StQP) consists of finding the largest or smallest value of a (possibly indefinite) quadratic form over the standard simplex which is the intersection of a hyperplane with the positive orthant. This NP-hard problem has several immediate real-world applications like the Maximum-Clique Problem, and it also occurs in a natural way as a subproblem in quadra...