Related papers: Continuity in Parametric Linear Programming
The effectiveness of utility-maximization techniques for portfolio management relies on our ability to estimate correctly the parameters of the dynamics of the underlying financial assets. In the setting of complete or incomplete financial…
In this paper we studied combinatorial problems with parameterized locally budgeted uncertainty. We are looking for a solutions set such that for any parameters vector there exists a solution in the set with robustness near optimal. The…
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…
We provide proof that the optimal value function of a convex parametrized optimization problem in Euclidean spaces is itself a convex function onto the extended real line.
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…
We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…
We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct:…
For an integer linear optimization (ILO) problem, persistency of its linear optimization (LO) relaxation is a property that for every optimal solution of the relaxation that assigns integer values to some variables, there exists an optimal…
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…
We present an open architecture for just-in-time code generation and dynamic code optimization that is flexible, customizable, and extensible. While previous research has primarily investigated functional aspects of such a system,…
Linear Programs (LP) are celebrated widely, particularly so in machine learning where they have allowed for effectively solving probabilistic inference tasks or imposing structure on end-to-end learning systems. Their potential might seem…
We study the problem of optimizing nonlinear objective functions over bipartite matchings. While the problem is generally intractable, we provide several efficient algorithms for it, including a deterministic algorithm for maximizing convex…
We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems.
We study a colourful generalization of the linear programming feasibility problem, comparing the algorithms introduced by Barany and Onn with new methods. We perform benchmarking on generic and ill-conditioned problems, as well as as…
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…
Let $\A$ be the operator which assigns to each $m \times n$ matrix-valued function on the unit circle with entries in $H^\infty + C$ its unique superoptimal approximant in the space of bounded analytic $m \times n$ matrix-valued functions…
This paper is concerned with the relationship between maximum principle and dynamic programming principle for risk-sensitive stochastic optimal control problems. Under the smooth assumption of the value function, relations among the adjoint…
We investigate the descriptional complexity of operations on semilinear sets. Roughly speaking, a semilinear set is the finite union of linear sets, which are built by constant and period vectors. The interesting parameters of a semilinear…
Semidefinite programs are convex optimisation problems involving a linear objective function and a domain of positive semidefinite matrices. Over the last two decades, they have become an indispensable tool in quantum information science.…
We consider a nonlinear pricing environment with private information. We provide profit guarantees (and associated mechanisms) that the seller can achieve across all possible distributions of willingness to pay of the buyers. With a…