Related papers: Strong Duality Theorem for Continuous-Time Linear …
Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply-rates are employed here for…
We prove the existence of strong and weak solutions to the semilinear wave equation with coefficients depending both on time and space variables, with continuous nonlinearity satisfying the sign condition. The uniqueness is proven under…
Using linear functional-based duality of modules, we generalize the syndrome decoding algorithm of linear codes over finite fields to those over finite commutative rings. Moreover, If the ring is local the algorithm is simplified by…
Separation is a classical problem in mathematics and computer science. It asks whether, given two sets belonging to some class, it is possible to separate them by another set of a smaller class. We present and discuss the separation problem…
We prove duality between the left and right fractional derivatives, independently on the type of fractional operator. Main result asserts that the right derivative of a function is the dual of the left derivative of the dual function or,…
Motivated by a growing list of nontraditional statistical estimation problems of the piecewise kind, this paper provides a survey of known results supplemented with new results for the class of piecewise linear-quadratic programs. These are…
In the theory of answer set programming, two groups of rules are called strongly equivalent if, informally speaking, they have the same meaning in any context. The relationship between strong equivalence and the propositional logic of…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
Recently, a new fractional derivative called the conformable fractional derivative is given on based basic limit definition derivative in [4]. Then, the fractional versions of chain rules, exponential functions, Gronwalls inequality,…
The Delsarte extremal problem for positive definite functions, originally introduced by Delsarte in coding theory to bound the size of error-correcting codes, has since found applications in diverse areas such as sphere packing, Fuglede's…
This paper studies parameterized stochastic optimization problems in finite discrete time that arise in many applications in operations research and mathematical finance. We prove the existence of solutions and the absence of a duality gap…
In this study, explicit differential equations representing commutative pairs of some well-known second-order linear time-varying systems have been derived. The commutativity of these systems are investigated by considering 30 second-order…
We investigate the convergence of the primal-dual algorithm for composite optimization problems when the objective functions are weakly convex. We introduce a modified duality gap function, which is a lower bound of the standard duality gap…
We formulate a refined theory of linear systems, using the methods of a previous paper, "A Theory of Branches for Algebraic Curves", and use it to give a geometric interpretation of the genus of an algebraic curve. Using principles of…
In the past years, deep learning models have been successfully applied in several cognitive tasks. Originally inspired by neuroscience, these models are specific examples of differentiable programs. In this paper we define and motivate…
In considering the reliability of numerical programs, it is normal to "limit our study to the semantics dealing with numerical precision" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that…
Linear programming has played a crucial role in shaping decision-making, resource allocation, and cost reduction in various domains. In this paper, we investigate the application of overparametrized neural networks and their implicit bias…
Much is known about when a locally optimal solution depends in a single-valued Lipschitz continuous way on the problem's parameters, including tilt perturbations. Much less is known, however, about when that solution and a uniquely…
In semidefinite programming the dual may fail to attain its optimal value and there could be a duality gap, i.e., the primal and dual optimal values may differ. In a striking paper, Ramana proposed a polynomial size extended dual that does…
The rate vs. distance problem is a long-standing open problem in coding theory. Recent papers have suggested a new way to tackle this problem by appealing to a new hierarchy of linear programs. If one can find good dual solutions to these…