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Discrete 2-convex functions
Springer Science and Business Media LLC - Tập 195 - Trang 831-854 - 2021
We focus on a new class of integrally convex functions which we call discrete 2-convex functions. Discrete 2-convexity generalizes known classes of integrally convex functions such as the well-established M-/M
$${}^\natural $$
-convex and L-/L
...... hiện toàn bộ
Characterization of TU games with stable cores by nested balancedness
Springer Science and Business Media LLC - - Trang 1-26 - 2021
A balanced transferable utility game (N, v) has a stable core if its core is externally stable, that is, if each imputation that is not in the core is dominated by some core element. Given two payoff allocations x and y, we say that x outvotes y via some coalition S of a feasible set if x dominates y via S and x allocates at least v(T) to any feasible T that is not contained in S. It turns out tha...... hiện toàn bộ
Generalized Chvátal-Gomory closures for integer programs with bounds on variables
Springer Science and Business Media LLC - Tập 190 - Trang 393-425 - 2020
Integer programming problems that arise in practice often involve decision variables with one or two sided bounds. In this paper, we consider a generalization of Chvátal-Gomory inequalities obtained by strengthening Chvátal-Gomory inequalities using the bounds on the variables. We prove that the closure of a rational polyhedron obtained after applying the generalized Chvátal-Gomory inequalities is...... hiện toàn bộ
A continuous deformation algorithm for variational inequality problems on polytopes
Springer Science and Business Media LLC - Tập 64 - Trang 103-122 - 1994
A continuous deformation algorithm is proposed for solving a variational inequality problem on a polytopeK. The algorithm embeds the polytopeK intoK× [0, ∞) and starts by applying a variable dimension algorithm onK× {0} until an approximate solution is found onK× {0}. Then by tracing the path of solutions of a system of equations the algorithm virtually follows a path of approximate solution inK× ...... hiện toàn bộ
Shapes and recession cones in mixed-integer convex representability
Springer Science and Business Media LLC - - Trang 1-14 - 2023
Mixed-integer convex representable (MICP-R) sets are those sets that can be represented exactly through a mixed-integer convex programming formulation. Following up on recent work by Lubin et al. (in: Eisenbrand (ed) Integer Programming and Combinatorial Optimization - 19th International Conference, Springer, Waterloo), (Math. Oper. Res. 47:720-749, 2022) we investigate structural geometric proper...... hiện toàn bộ
Robust solutions of Linear Programming problems contaminated with uncertain data
Springer Science and Business Media LLC - Tập 88 - Trang 411-424 - 2000
Optimal solutions of Linear Programming problems may become severely infeasible if the nominal data is slightly perturbed. We demonstrate this phenomenon by studying 90 LPs from the well-known NETLIB collection. We then apply the Robust Optimization methodology (Ben-Tal and Nemirovski [1–3]; El Ghaoui et al. [5, 6]) to produce “robust” solutions of the above LPs which are in a sense immuned agains...... hiện toàn bộ
A note on Fejér-monotone sequences in product spaces and its applications to the dual convergence of augmented Lagrangian methods
Springer Science and Business Media LLC - - 2014
In a recent Math. Program. paper, Eckstein and Silva proposed a new error criterion for the approximate solutions of augmented Lagrangian subproblems. Based on a saddle-point formulation of the primal and dual problems, they proved that dual sequences generated by augmented Lagrangians under this error criterion are bounded and that their limit points are dual solutions. In this note, we prove a n...... hiện toàn bộ
Non-monotone trust region methods for nonlinear equality constrained optimization without a penalty function
Springer Science and Business Media LLC - Tập 95 - Trang 103-135 - 2003
We propose and analyze a class of penalty-function-free nonmonotone trust-region methods for nonlinear equality constrained optimization problems. The algorithmic framework yields global convergence without using a merit function and allows nonmonotonicity independently for both, the constraint violation and the value of the Lagrangian function. Similar to the Byrd–Omojokun class of algorithms, e...... hiện toàn bộ
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