An optimal control problem is studied, in which the state is required to remain in a compact set S. A control feedback law is constructed which, for given ε > 0, produces ε-optimal trajectories that satisfy the state constraint universally with respect to all initial conditions in S. The construction relies upon a constraint removal technique which utilizes geometric properties of inner approxi...

We present an approximation algorithm for the shortest descending path problem. Given a source s and a destination t on a terrain, a shortest descending path from s to t is a path of minimum Euclidean length on the terrain subject to the constraint that the height decreases monotonically as we traverse that path from s to t. Given any ε ∈ (0, 1), our algorithm returns in O(n log(n/ε)) time a de...

Many previous Sum-of-Squares (SOS) lower bounds for CSPs had two deficiencies related to global constraints. First, they were not able to support a “cardinality constraint”, as in, say, the Min-Bisection problem. Second, while the pseudoexpectation of the objective function was shown to have some value β, it did not necessarily actually “satisfy” the constraint “objective = β”. In this paper we...

Hazardous waste location-routing problems are of importance due to the potential risk for nearby residents and the environment. In this paper, an improved mathematical formulation is developed based upon a multi-objective mixed integer programming approach. The model aims at assisting decision makers in selecting locations for different facilities including treatment plants, recycling plants an...

In this paper, a bi-objective model is proposed for designing a pre-positioning network of pharmaceutical supplies considering their limited shelf-life. The presented model aims to consider both cost efficiency and responsiveness by minimization of total cost and the maximum amount of unmet demand under uncertainties in demand and supply sides’ data. Moreover, for effective distribution of reli...

This paper investigates the following natural greedy procedure for clustering in the bi-criterion setting: iteratively grow a set of centers, in each round adding the center from a candidate set that maximally decreases clustering cost. In the case of k-medians and k-means, the key results are as follows. • When the method considers all data points as candidate centers, then selecting O(k log(1...

An instance of a constraint satisfaction problem (CSP) is variable k-consistent if any subinstance with at most k variables has a solution. For a fixed constraint language L, ρk(L) is the largest ratio such that any variable k-consistent instance has a solution that satisfies at least a fraction of ρk(L) of the constraints. We provide an expression for the limit ρ(L) := limk→∞ ρk(L), and show t...

Abstract. To deal with the divergence-free constraint in a double curl problem: curlμ−1curlu = f and div εu = 0 in Ω, where μ and ε represent the physical properties of the materials occupying Ω, we develop a δ-regularization method: curlμcurluδ + δεuδ = f to completely ignore the divergence-free constraint div εu = 0. It is shown that uδ converges to u in H(curl ; Ω) norm as δ → 0. The edge fi...