We apply theta body relaxations to the $K_i$ cover problem and use this to show polynomial time solvability for certain classes of graphs. In particular, we give an effective relaxation where all $K_i$-$p$-hole facets are valid, addressing an open question of Conforti et al \cite{conforti}. For the triangle free problem, we show for $K_n$ that … Read more
In this paper we consider $l_0$ regularized convex cone programming problems. In particular, we first propose an iterative hard thresholding (IHT) method and its variant for solving $l_0$ regularized box constrained convex programming. We show that the sequence generated by these methods converges to a local minimizer. Also, we establish the iteration complexity of the … Read more
The expected utility knapsack problem is to pick a set of items whose values are described by random variables so as to maximize the expected utility of the total value of the items picked while satisfying a constraint on the total weight of items picked. We consider the following solution approach for this problem: (i) … Read more
This paper considers a quadratically-constrained cardinality minimization problem with applications to digital filter design, subset selection for linear regression, and portfolio selection. Two relaxations are investigated: the continuous relaxation of a mixed integer formulation, and an optimized diagonal relaxation that exploits a simple special case of the problem. For the continuous relaxation, an absolute upper … Read more
The minimum concave cost network flow problem (MCCNFP) is NP-hard, but efficient polynomial-time algorithms exist for some special cases such as the uncapacitated lot-sizing problem and many of its variants. We study the MCCNFP over a grid network with a general nonnegative separable concave cost function. We show that this problem is polynomially solvable when … Read more
This position paper reflects on the generalization of adaptive methods for Constraint Programming (CP) solving mechanisms, and suggests the use of application-oriented descriptions as a means to broaden CP adoption in the industry. We regard as an adaptive method any procedure that modifies the behavior of the solving process according to previous experience gathered from … Read more
We provide a family of polytopes P in [0, 1]^n whose Gomory-Chvátal rank is at least ((1 + 1/6)n – 4). Citation Rutcor 640 Bartholomew Road Piscataway, NJ 08854-8003 , July,2012 Article Download View A family of polytopes in the 0/1-cube with Gomory-Chvátal rank at least ((1+1/6)n – 4)
In this paper, we study self-avoiding walks of a given length on a graph. We consider a formulation of this problem as a binary linear program. We analyze the polyhedral structure of the underlying polytope and describe valid inequalities. Proofs for their facial properties for certain special cases are given. In a variation of this … Read more
In a cross-dock facility, goods are moved by forklift from incoming truck platforms (strip doors) to temporary holding areas and then to outgoing truck platforms (stack doors) or directly from strip doors to stack doors. Costs within the cross-dock may be minimized by appropriate assignment of strip doors to incoming trucks and stack doors to … Read more
This paper considers robust dynamic optimization problems, where the unknown parameters are modeled as uncertainty sets. We seek to bridge two classical paradigms for solving such problems, namely (1) Dynamic Programming (DP), and (2) policies parameterized in model uncertainties (also known as decision rules), obtained by solving tractable convex optimization problems. We provide a set … Read more