We consider two-stage quadratic integer programs with stochastic right-hand sides, and present an equivalent reformulation using value functions. We first derive some basic properties of value functions of quadratic integer programs. We then propose a two-phase solution approach. The first phase constructs the value functions of quadratic integer programs in both stages. The second phase solves...

In this article we present a parametric branch and bound algorithm for computation of optimal and suboptimal solutions to parametric mixed-integer quadratic programs and parametric mixed-integer linear programs. The algorithm returns an optimal or suboptimal parametric solution with the level of suboptimality requested by the user. An interesting application of the proposed parametric branch an...

In this paper, we study the problem of technical transient gas network optimization, which can be considered as a minimum cost flow problem with a nonlinear objective function and additional nonlinear constraints on the network arcs. Applying an implicit box scheme to the isothermal Euler equation, we derive a mixed integer nonlinear program. This is solved by means of a combination of (i) a no...

In this paper we integrate at the tactical level two decision problems arising in container terminals: the berth allocation problem, which consists of assigning and scheduling incoming ships to berthing positions, and the quay crane assignment problem, which assigns to incoming ships a certain QC profile (i.e. number of quay cranes per working shift). We present two formulations: a mixed intege...

Control of dynamical systems gets considerably harder with an increasing number of control variables. Especially when the control variables are restricted to integer values, the solution is of combinatorial complexity. An example of such systems are Digital Hydraulic Drives, where several cylinders contribute to the output torque independently. In this work we present an optimal control approac...

In this paper, we consider an Airport Gate Assignment Problem that dynamically assigns airport gates to scheduled ights based on passengers' daily origin and destination ow data. The objective of the problem is to minimize the overall connection times that passengers walk to catch their connection ights. We formulate this problem as a mixed 0-1 quadratic integer programming problem and then ref...

This paper proposes a method for eliminating multicollinearity from linear regression models. Specifically, we select the best subset of explanatory variables subject to the upper bound on the condition number of the correlation matrix of selected variables. We first develop a cutting plane algorithm that, to approximate the condition number constraint, iteratively appends valid inequalities to...

This paper is concerned with solving nonconvex learning problems with folded concave penalty. Despite that their global solutions entail desirable statistical properties, there lack optimization techniques that guarantee global optimality in a general setting. In this paper, we show that a class of nonconvex learning problems are equivalent to general quadratic programs. This equivalence facili...