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- Natashia Boland, Andrew C. Eberhard
- Math. Program.
- 2015

We consider the augmented Lagrangian dual for integer programming, and provide a primal characterization of the resulting bound. As a corollary, we obtain proof that the augmented Lagrangian is a… (More)

- Natashia Boland, Jeffrey Christiansen, Brian Dandurand, Andrew C. Eberhard, Fabricio Oliveira
- Math. Program.
- 2018

We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly… (More)

- Andrew C. Eberhard, Robert Bruno Wenczel
- SIAM Journal on Optimization
- 2009

In this paper we study some second order conditions that may be added to the first order nessessary optimality condition 0 ∈ ∂pf(x̄) (with ∂pf denoting the proximal subdifferential) in order to… (More)

We establish maximality of the sum of two maximal monotone operators in general Banach space, assuming only the Rockafellar qualification assumption. This resolves, affirmatively, a thirty-five year… (More)

This paper mainly concerns deriving first-order and second-order necessary (and partly sufficient) optimality conditions for a general class of constrained optimization problems via smoothing… (More)

- Natashia Boland, Andrew C. Eberhard, Faramroze G. Engineer, Angelos Tsoukalas
- SIAM Journal on Optimization
- 2012

The feasibility pump is a recent, highly successful heuristic for general mixed integer linear programming problems. We show that the feasibility pump heuristic can be interpreted as a discrete… (More)

A utility function u : R+ := { x ∈ R | x ≥ 0 for all i} → R := R∪{−∞} is often used to reflect the preference structure with respect to possible consumption of n commodities, denoted by a vector x ∈… (More)

- Natashia Boland, Andrew C. Eberhard, Faramroze G. Engineer, Matteo Fischetti, Martin W. P. Savelsbergh, Angelos Tsoukalas
- Math. Program. Comput.
- 2014

The feasibility pump (FP) has proved to be an effective method for finding feasible solutions to mixed integer programming problems. FP iterates between a rounding procedure and a projection… (More)

It is shown that various first and second order derivatives of the Fitzpatrick and Penot representative functions for a maximal monotone operator T, in a reflexive Banach space, can be used to… (More)