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Segmenting an image into multiple components is a central task in computer vision. In many practical scenarios, prior knowledge about plausible components is available. Incorporating such prior knowledge into models and algorithms for image…
In this paper we study constraint qualifications and optimality conditions for bilevel programming problems. We strive to derive checkable constraint qualifications in terms of problem data and applicable optimality conditions. For the…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
Outer approximation methods have long been employed to tackle a variety of optimization problems, including linear programming, in the 1960s, and continue to be effective for solving variational inequalities, general convex problems, as…
We consider the global optimization of nonconvex mixed-integer quadratic programs with linear equality constraints. In particular, we present a new class of convex quadratic relaxations which are derived via quadratic cuts. To construct…
Logic-Based Benders Decomposition (LBBD) and its Branch-and-Cut variant, namely Branch-and-Check, enjoy an extensive applicability on a broad variety of problems, including scheduling. Although LBBD offers problem-specific cuts to impose…
In high-stakes engineering applications, optimization algorithms must come with provable worst-case guarantees over a mathematically defined class of problems. Designing for the worst case, however, inevitably sacrifices performance on the…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
Many relevant applications from diverse areas such as marketing, wildlife conservation, or defending critical infrastructure can be modeled as interdiction games. In this work, we introduce interdiction games whose objective is a monotone…
Our aim is to explain mathematical programs with equilibrium constraints (MPECs), motivate them through applications, present the main equivalent formulations of equilibrium constraints, and summarize the basic existence theory for optimal…
We study the complexity of cutting planes and branching schemes from a theoretical point of view. We give some rigorous underpinnings to the empirically observed phenomenon that combining cutting planes and branching into a branch-and-cut…
Current state-of-the-art methods for solving discrete optimization problems are usually restricted to convex settings. In this paper, we propose a general approach based on cutting planes for solving nonlinear, possibly nonconvex, binary…
The linear complementarity problem is a continuous optimization problem that generalizes convex quadratic programming, Nash equilibria of bimatrix games and several such problems. This paper presents a continuous optimization formulation…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
Linear bilevel programs (linear BLPs) have been widely used in computational mathematics and optimization in several applications. Single-level reformulation for linear BLPs replaces the lower-level linear program with its…
We study a class of bilevel integer programs with second-order cone constraints at the upper level and a convex quadratic objective and linear constraints at the lower level. We develop disjunctive cuts to separate bilevel infeasible points…
It has been shown that the parallel Lattice Linear Predicate (LLP) algorithm solves many combinatorial optimization problems such as the shortest path problem, the stable marriage problem and the market clearing price problem. In this…
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine…
In multiobjective optimization, most branch and bound algorithms provide the decision maker with the whole Pareto front, and then decision maker could select a single solution finally. However, if the number of objectives is large, the…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…