Related papers: Generating Asymptotically Non-Terminating Initial …
We study non-stationary stochastic processes arising from sequential dynamical systems built on maps with a neutral fixed points and prove the existence of Extreme Value Laws for such processes. We use an approach developed in \cite{FFV16},…
We consider the infinite dimensional linear programming (inf-LP) approach for solving stochastic control problems. The inf-LP corresponding to problems with uncountable state and input spaces is in general computationally intractable. By…
We propose a new kind of stochastic absolute value equations involving absolute values of variables. By utilizing an equivalence relation to stochastic bilinear program, we investigate the expected value formulation for the proposed…
Parametric high-dimensional regression analysis requires the usage of regularization terms to get interpretable models. The respective estimators can be regarded as regularized M-functionals which are naturally highly nonlinear. We study…
We provide a complete combinatorial and asymptotic analysis of positive linear systems of equations in one catalytic variable that appear in several combinatorial problems such as in lattice path counting or stack-sortable permutation…
An integer program (IP) with a finite number of feasible solutions may have an unbounded linear programming relaxation if it contains irrational parameters, due to implicit constraints enforced by the irrational numbers. We show that those…
This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…
The extension of classical imperative programs with real-valued random variables and random branching gives rise to probabilistic programs. The termination problem is one of the most fundamental liveness properties for such programs. The…
In this paper, we study weakly nonlinear boundary value problems on infinite intervals. For such problems, we provide criteria for the existence of solutions as well as a qualitative description of the behavior of solutions depending on a…
We develop and generalize the theory of extreme value for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this setting. We apply our results to non-autonomous dynamical…
Initial value problems -- a system of ordinary differential equations and corresponding initial conditions -- can be used to describe many physical phenomena including those arise in classical mechanics. We have developed a novel approach…
This paper proposes a model, the linear model, for randomly generating logic programs with low density of rules and investigates statistical properties of such random logic programs. It is mathematically shown that the average number of…
We introduce and study the infinite dimensional linear programming problem which along with its dual allows one to characterize the optimal value of the deterministic long-run average optimal control problem in the general case when the…
This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These…
On the one hand, termination analysis of logic programs is now a fairly established research topic within the logic programming community. On the other hand, non-termination analysis seems to remain a much less attractive subject. If we…
Some results are proved concerning asymptotic and deficient values in connection with the second order linear differential equation $y'' + Ay = 0$, in which the coefficient $A$ is entire.
We study optimal decision policies for integer linear programs with a fixed feasible set and varying cost vectors, represented as linear decision trees. Once synthesized for a given feasible set, they return an optimal solution for any…
We present a novel analysis of semidefinite programs (SDPs) with positive duality gaps, i.e. different optimal values in the primal and dual problems. These SDPs are extremely pathological, often unsolvable, and also serve as models of more…
We consider a broad class of dynamic programming (DP) problems that involve a partially linear structure and some positivity properties in their system equation and cost function. We address deterministic and stochastic problems, possibly…
We present a method for generating training data for reinforcement learning with verifiable rewards to improve small open-weights language models on mathematical tasks. Existing data generation approaches rely on open-loop pipelines and…