Related papers: A Mathematical Theory of Co-Design
Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…
We focus on designing combinatorial algorithms for the Capacitated Network Design problem (Cap-SNDP). The Cap-SNDP is the problem of satisfying connectivity requirements when edges have costs and hard capacities. We begin by showing that…
In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…
Motivated by the grid search method and Bayesian optimization, we introduce the concept of contractibility and its applications in model-based optimization. First, a basic framework of contraction methods is established to construct a…
We introduce a novel approach to reduce the computational effort of solving mixed-integer convex chance constrained programs through the scenario approach. Instead of reducing the number of required scenarios, we directly minimize the…
We consider the following shared-resource scheduling problem: Given a set of jobs $J$, for each $j\in J$ we must schedule a job-specific processing volume of $v_j>0$. A total resource of $1$ is available at any time. Jobs have a resource…
This is a survey on the use of low-degree polynomials to predict and explain the apparent statistical-computational tradeoffs in a variety of average-case computational problems. In a nutshell, this framework measures the complexity of a…
We consider the makespan minimization coupled-tasks problem in presence of compatibility constraints with a specified topology. In particular, we focus on stretched coupled-tasks, i.e. coupled-tasks having the same sub-tasks execution time…
We revisit a classical problem in transportation, known as the continuous (bilevel) network design problem, CNDP for short. We are given a graph for which the latency of each edge depends on the ratio of the edge flow and the capacity…
This is the first paper that provides a systematic treatment of the $r$-dimensional PTE problem in additive number theory, abbreviated by PTE$_r$, through its connection with combinatorial design theory, the branch of combinatorial…
In machine learning and big data, the optimization objectives based on set-cover, entropy, diversity, influence, feature selection, etc. are commonly modeled as submodular functions. Submodular (function) maximization is generally NP-hard,…
In this paper, we consider the problem of scheduling an application on a parallel computational platform. The application is a particular task graph, either a linear chain of tasks, or a set of independent tasks. The platform is made of…
We consider a network topology design problem in which an initial undirected graph underlying the network is given and the objective is to select a set of edges to add to the graph to optimize the coherence of the resulting network. We show…
The family of graphs that can be constructed from isolated vertices by disjoint union and graph join operations are called cographs. These graphs can be represented in a tree-like representation termed parse tree or cotree. In this paper,…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
This thesis is concerned with the design of distributed algorithms for solving optimization problems. We consider networks where each node has exclusive access to a cost function, and design algorithms that make all nodes cooperate to find…
We study stochastic combinatorial optimization problems where the objective is to minimize the expected maximum load (a.k.a.\ the makespan). In this framework, we have a set of $n$ tasks and $m$ resources, where each task $j$ uses some…
We propose three novel mathematical optimization formulations that solve the same two-type heterogeneous multiprocessor scheduling problem for a real-time taskset with hard constraints. Our formulations are based on a global scheduling…
The Promise Constraint Satisfaction Problem (PCSP for short) is a generalization of the well-studied Constraint Satisfaction Problem (CSP). The PCSP has its roots in such classic problems as the Approximate Graph Coloring and the…
Designing component-based constraint solvers is a complex problem. Some components are required, some are optional and there are interdependencies between the components. Because of this, previous approaches to solver design and…