A new lift-and-project operator

In this paper, we analyze the strength of split cuts in a lift-and-project framework. We first observe that the Lovasz-Schrijver and Sherali-Adams lift-and-project operator hierarchies can be viewed as applying specific 0-1 split cuts to an appropriate extended formulation and demonstrate how to strengthen these hierarchies using additional split cuts. More precisely, we define a … Read more

Distributionally Robust Logistic Regression

This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If the radius of this ball is chosen judiciously, we can guarantee that it contains the unknown data-generating distribution with high … Read more

Manifold Sampling for L1 Nonconvex Optimization

We present a new algorithm, called manifold sampling, for the unconstrained minimization of a nonsmooth composite function $h\circ F$ when $h$ has known structure. In particular, by classifying points in the domain of the nonsmooth function $h$ into manifolds, we adapt search directions within a trust-region framework based on knowledge of manifolds intersecting the current … Read more

Adaptive Elective Surgery Planning Under Duration and Length-Of-Stay Uncertainty: A Robust Optimization Approach

Scheduling elective surgeries is a complicated task due to the coupled effect of multiple sources of uncertainty and the impact of the proposed schedule on the downstream units. In this paper, we propose an adaptive robust optimization model to address the existing uncertainty in surgery duration and length-of-stay in the surgical intensive care unit. The … Read more

On Cournot-Nash-Walras equilibria and their computation

This paper considers a model of Cournot-Nash-Walras (CNW) equilibrium where the Cournot-Nash concept is used to capture equilibrium of an oligopolistic market with non-cooperative players/ rms who share a certain amount of a so-called rare resource needed for their production, and the Walras equilibrium determines the price of that rare resource. We prove the existence of … Read more

Strong slopes of a vector-valued map and applications in the study of error bounds, weak sharp minima and calmness

Using Hiriart-Urruty’s signed distance function, we present new definitions of strong slopes for a vector-valued map recently introduced in [E.M. Bednarczuk, A.Y., Kruger, Error bounds for vector-valued functions on metric spaces. Vietnam J. Math. 40 (2012), no. 2-3, 165-180]. With the new presentation, we are able to show that these slopes enjoy most properties of … Read more

Location Routing Problems on Simple Graphs

This paper addresses combined location/routing problems defined on trees. Several problems are studied, which consider service demand both at the vertices and the edges of the input tree. Greedy type optimal heuristics are presented for the cases when all vertices have to be visited and facilities have no set-up costs. Facilities set-up costs can also … Read more

Optimization over Sparse Symmetric Sets via a Nonmonotone Projected Gradient Method

We consider the problem of minimizing a Lipschitz differentiable function over a class of sparse symmetric sets that has wide applications in engineering and science. For this problem, it is known that any accumulation point of the classical projected gradient (PG) method with a constant stepsize $1/L$ satisfies the $L$-stationarity optimality condition that was introduced … Read more

A Study of Three-Period Ramp-Up Polytope

We study the polyhedron of the unit commitment problem, and consider a relaxation involving the ramping constraints. We study the three-period ramp-up polytope, and describe the convex-hull using a new class of inequalities. Citation [1] J. Ostrowski, M. F. Anjos, and A. Vannelli, \Tight mixed integer linear programming formulations for the unit commitment problem,” Power … Read more

Degeneracy in Maximal Clique Decomposition for Semidefinite Programs

Exploiting sparsity in Semidefinite Programs (SDP) is critical to solving large-scale problems. The chordal completion based maximal clique decomposition is the preferred approach for exploiting sparsity in SDPs. In this paper, we show that the maximal clique-based SDP decomposition is primal degenerate when the SDP has a low rank solution. We also derive conditions under … Read more