Abstract In this paper, we propose a novel and effective approximation method for finding the value function general utility maximization with closed convex control constraints partial information. Using separation principle weak duality relation, transform stochastic maximum of fully observable dual problem into an equivalent error minimization find tight lower upper bounds its approximate val...

We devise a constant-factor approximation algorithm for the maximization version of edge-disjoint paths problem if supply graph together with demand edges form planar graph. By duality this is equivalent to packing cuts in such that each cut contains exactly one edge. also show natural linear programming relaxations have constant integrality gap, yielding an approximate max-multiflow min-multic...

The present paper is devoted to the duality theory for convex optimal control problem of second-order differential inclusions with periodic boundary conditions. First, we use an auxiliary discrete-approximate and focus on formulating sufficient conditions optimality problem. Then, concentrate that exists in establish a dual prove Euler-Lagrange are relations both primal problems. Finally, consi...

Semidefinite relaxations of certain combinatorial optimization problems lead to approximation algorithms with performance guarantees. For large-scale problems, it may not be computationally feasible to solve the semidefinite relaxations to optimality. In this paper, we investigate the effect on the performance guarantees of an approximate solution to the semidefinite relaxation for MaxCut, Max2...

In order to show existence of solutions for linear elliptic problems with measure data, a first classical method, due to Stampacchia, is to use a duality argument (and a regularity result for elliptic problems). Another classical method is to pass to the limit on approximate solutions obtained with regular data (converging towards the measure data). A third method is presented. It consists to p...

The objective of the paper is to investigate the approximate controllability property of a linear stochastic control system with values in a separable real Hilbert space. In a first step we prove the existence and uniqueness for the solution of the dual linear backward stochastic differential equation. This equation has the particularity that in addition to an unbounded operator acting on the Y...

The tensors of curvature play an important role in differential geometry. In surface theory (1990), it is determined by the derivative of unit normal vectors of tangent spaces of the underlying surface. However every geometric object in computation is a discrete model. We can only approximate them. In estimating the curvature on polyhedral surfaces, how to approximate normal vectors is a crucia...

Discrete Duality Finite Volume (DDFV) schemes have recently been developed in 2D to approximate nonlinear diffusion problems on general meshes. In this paper, a 3D extension of these schemes is proposed. The construction of this extension is detailed and its main properties are proved: a priori bounds, well-posedness and error estimates. The practical implementation of this scheme is easy. Nume...

Approximately dual frames are studied in the Hilbert space setting. Approximate duals are easier to construct than classical dual frames, and can be tailored to yield almost perfect reconstruction. Bounds on the deviation from perfect reconstruction are obtained for approximately dual frames constructed via perturbation theory. An alternative bound is derived for the rich class of Gabor frames,...

An ε-approximate incidence between a point and some geometric object (line, circle, plane, sphere) occurs when the point and the object lie at distance at most ε from each other. Given a set of points and a set of objects, computing the approximate incidences between them is a major step in many database and web-based applications in computer vision and graphics, including robust model fitting,...