In this paper, we present a novel penalty model called ExPen for optimization over the Stiefel manifold. Different from existing penalty functions for orthogonality constraints, ExPen adopts a smooth penalty function without using any first-order derivative of the objective function. We show that all the first-order stationary points of ExPen with a sufficiently large penalty … Read more
We investigate the concept of adjustability — the difference in objective values between two types of dynamic robust optimization formulations: one where (static) decisions are made before uncertainty realization, and one where uncertainty is resolved before (adjustable) decisions. This difference reflects the value of information and decision timing in optimization under uncertainty, and is related … Read more
This work addresses optimal control problems governed by a linear time-dependent partial differential equation (PDE) as well as integer constraints on the control. Moreover, partial observations are assumed in the objective function. The resulting problem poses several numerical challenges due to the mixture of combinatorial aspects, induced by integer variables, and large scale linear algebra … Read more
We investigate questions related to the set $\mathcal{SEP}_d$ consisting of the linear maps $\rho$ acting on $\mathbb{C}^d\otimes \mathbb{C}^d$ that can be written as a convex combination of rank one matrices of the form $xx^*\otimes yy^*$. Such maps are known in quantum information theory as the separable bipartite states, while nonseparable states are called entangled. In … Read more
In this paper we study the rank of polytopes contained in the 0-1 cube with respect to $t$-branch split cuts and $t$-dimensional lattice cuts for a fixed positive integer $t$. These inequalities are the same as split cuts when $t=1$ and generalize split cuts when $t > 1$. For polytopes contained in the $n$-dimensional 0-1 … Read more
The problem of interest is the minimization of a nonlinear function subject to nonlinear equality constraints using a sequential quadratic programming (SQP) method. The minimization must be performed while observing only noisy evaluations of the objective and constraint functions. In order to obtain stability, the classical SQP method is modified by relaxing the standard Armijo … Read more
We propose robust optimization models and their tractable approximations that cater for ambiguity-averse decision makers whose underlying risk preferences are consistent with constant absolute risk aversion (CARA). Specifically, we focus on maximizing the worst-case expected exponential utility where the underlying uncertainty is generated from a set of stochastically independent factors with ambiguous marginals. To obtain … Read more
Markov decision process (MDP) models have been used to obtain non-stationary optimal decision rules in various applications, such as treatment planning in medical decision making. However, in practice, decision makers may prefer other strategies that are not statistically different from the optimal decision rules. To benefit from the decision makers’ expertise and provide flexibility in … Read more
Many real-life optimization problems frequently contain one or more constraints or objectives for which there are no explicit formulas. If data is however available, these data can be used to learn the constraints. The benefits of this approach are clearly seen, however there is a need for this process to be carried out in a … Read more
This paper presents a proximal bundle (PB) framework based on a generic bundle update scheme for solving the hybrid convex composite optimization (HCCO) problem and establishes a common iteration-complexity bound for any variant belonging to it. As a consequence, iteration-complexity bounds for three PB variants based on different bundle update schemes are obtained in the … Read more