This paper considers the solution of tree-structured Quadratic Programs (QPs) as they may arise in multi- stage Model Predictive Control (MPC). In this context, sampling the uncertainty on prescribed decision points gives rise to different scenarios that are linked to each other via the so-called non-anticipativity constraints. Previous work suggests to dualize these constraints and … Read more
In this paper we consider the minimization of a continuous function that is potentially not differentiable or not twice differentiable on the boundary of the feasible region. By exploiting an interior point technique, we present first- and second-order optimality conditions for this problem that reduces to classical ones when the derivative on the boundary is … Read more
A usual way to collect data in a Wireless Sensor Network (WSN) is by the support of a special agent, called data mule, that moves between sensor nodes and performs all communication between them. In this work, the focus is on the construction of the route that the data mule must follow to serve all … Read more
A distributionally robust joint chance constraint involves a set of uncertain linear inequalities which can be violated up to a given probability threshold $\epsilon$, over a given family of probability distributions of the uncertain parameters. A conservative approximation of a joint chance constraint, often referred to as a Bonferroni approximation, uses the union bound to … Read more
The alternating direction method of multipliers (ADMM) is a popular method for the separable convex programming with linear constraints, and the proximal ADMM is its important variant. Previous studies show that the relaxation factor $\gamma\in (0, \frac{1+\sqrt{5}}{2})$ by Fortin and Glowinski for the ADMM is also valid for the proximal ADMM. In this paper, we … Read more
We study the problem of computing weighted analytic center for system of linear matrix inequality constraints. The problem can be solved using the Standard Newton’s method. However, this approach requires that a starting point in the interior point of the feasible region be given or a Phase I problem be solved. We address the problem … Read more
Consensus optimization has received considerable attention in recent years. A number of decentralized algorithms have been proposed for {convex} consensus optimization. However, to the behaviors or consensus \emph{nonconvex} optimization, our understanding is more limited. When we lose convexity, we cannot hope our algorithms always return global solutions though they sometimes still do sometimes. Somewhat surprisingly, … Read more
In this paper, we develop a Parameterized Proximal Point Algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent with a worst-case $O(1/t)$ convergence rate, where $t$ is the iteration number. By properly choosing the algorithm parameters, numerical experiments … Read more
This paper presents a mixed-integer quadratically constrained programming (MIQCP) formulation for B-spline constraints. The formulation can be used to obtain an exact MIQCP reformulation of any spline-constrained optimization problem, provided that the polynomial spline functions are continuous. This reformulation allows practitioners to use a general-purpose MIQCP solver, instead of a special-purpose spline solver, when solving … Read more
A lower bound for a finite-scenario-based chance-constrained program is the quantile value corresponding to the sorted optimal objective values of scenario subproblems. This quantile bound can be improved by grouping subsets of scenarios at the expense of solving larger subproblems. The quality of the bound depends on how the scenarios are grouped. In this paper, … Read more