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We extend a primal-dual fixed point algorithm (PDFP) proposed in [5] to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP…
While globally optimal solutions to many convex programs can be computed efficiently in polynomial time, this is, in general, not possible for nonconvex optimization problems. Therefore, locally optimal approaches or other efficient…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing…
Advances in mobile computing technologies have made it possible to monitor and apply data-driven interventions across complex systems in real time. Markov decision processes (MDPs) are the primary model for sequential decision problems with…
Maximum Probability Framework, powered by Maximum Probability Theorem, is a recent theoretical development in artificial intelligence, aiming to formally define probabilistic models, guiding development of objective functions, and…
Value iteration is a well-known method of solving Markov Decision Processes (MDPs) that is simple to implement and boasts strong theoretical convergence guarantees. However, the computational cost of value iteration quickly becomes…
Value iteration is a commonly used and empirically competitive method in solving many Markov decision process problems. However, it is known that value iteration has only pseudo-polynomial complexity in general. We establish a somewhat…
We consider the numerical approximation of acoustic wave propagation problems by mixed BDM(k+1)-P(k) finite elements on unstructured meshes. Optimal convergence of the discrete velocity and super-convergence of the pressure by one order are…
The increasing demand for larger and higher fidelity simulations has made Adaptive Mesh Refinement (AMR) and unstructured mesh techniques essential to focus compute effort and memory cost on just the areas of interest in the simulation…
Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are…
This paper formalizes path planning problem for a group of heterogeneous Dubins vehicles performing tasks in a remote fashion and develops a memetic algorithm-based method to effectively produce the paths. In the setting, the vehicles are…
Semidefinite programs (SDPs) are a fundamental class of optimization problems with important recent applications in approximation algorithms, quantum complexity, robust learning, algorithmic rounding, and adversarial deep learning. This…
We take an existing implementation of an algorithm for the maximum clique problem and modify it so that we can distribute it over an ad-hoc cluster of machines. Our goal was to achieve a significant speedup in performance with minimal…
The COVID-19 pandemic has been a recent example for the spread of a harmful contagion in large populations. Moreover, the spread of harmful contagions is not only restricted to an infectious disease, but is also relevant to computer viruses…
This research explores the application of a genetic algorithm metaheuristic enriched by the wisdom of crowds in order to address the NP-Complete matrix domination problem (henceforth: TMDP) which is itself a constraint on related problems…
We propose a method to optimize the representation and distinguishability of samples from two probability distributions, by maximizing the estimated power of a statistical test based on the maximum mean discrepancy (MMD). This optimized MMD…
There are no computationally feasible algorithms that provide solutions to the finite horizon Risk-sensitive Constrained Markov Decision Process (Risk-CMDP) problem, even for problems with moderate horizon. With an aim to design the same,…
In this paper, the utilization of mobile devices (MDs) as decode-and-forward relays in a device-to-device assisted virtual MIMO (VMIMO) system is studied. Single antenna MDs are randomly distributed on a 2D plane according to a Poisson…
Policy Iteration (PI) is a widely used family of algorithms to compute optimal policies for Markov Decision Problems (MDPs). We derive upper bounds on the running time of PI on Deterministic MDPs (DMDPs): the class of MDPs in which every…
Set partitioning is a key component of many algorithms in machine learning, signal processing, and communications. In general, the problem of finding a partition that minimizes a given impurity (loss function) is NP-hard. As such, there…