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We present a general technique for approximating bicriteria minimization problems with positive-valued, polynomially computable objective functions. Given $0<\epsilon\leq1$ and a polynomial-time $\alpha$-approximation algorithm for the…
We study a class of projective transformations of spectraplexes associated with self-dual cones and, on this basis, propose a polynomial-time algorithm for convex feasibility problems with positive definite constraints. At each iteration of…
Energy functions offer natural extensions of controllability and observability Gramians to nonlinear systems, enabling various applications such as computing reachable sets, optimizing actuator and sensor placement, performing balanced…
Nowadays hybrid evolutionary algorithms, i.e, heuristic search algorithms combining several mutation operators some of which are meant to implement stochastically a well known technique designed for the specific problem in question while…
We present a first theoretical analysis of the power of polynomial-time preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability,…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
Since its inception in the mid-60s, the inventory staggering problem has been explored and exploited in a wide range of application domains, such as production planning, stock control systems, warehousing, and aerospace/defense logistics.…
In some important application areas of hard real-time systems, preemptive sporadic tasks with harmonic periods and constraint deadlines running upon a uni-processor platform play an important role. We propose a new algorithm for determining…
We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We consider extensions of the Shannon relative entropy, referred to as $f$-divergences.Three classical related computational problems are typically associated with these divergences: (a) estimation from moments, (b) computing normalizing…
In this paper we present new algorithms and analysis for the linear inverse sensor placement and scheduling problems over multiple time instances with power and communications constraints. The proposed algorithms, which deal directly with…
The Restricted Assignment Problem is a prominent special case of Scheduling on Parallel Unrelated Machines. For the strongest known linear programming relaxation, the configuration LP, we improve the non-constructive bound on its…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
In the problem called single resource constraint scheduling, we are given $m$ identical machines and a set of jobs, each needing one machine to be processed as well as a share of a limited renewable resource $R$. A schedule of these jobs is…
In this paper, we propose a framework based on sum-of-squares programming to design iterative first-order optimization algorithms for smooth and strongly convex problems. Our starting point is to develop a polynomial matrix inequality as a…
We extend the concept of polynomial time approximation algorithms to apply to problems for hierarchically specified graphs, many of which are PSPACE-complete. Assuming P != PSPACE, the existence or nonexistence of such efficient…
Finding a \emph{single} best solution is the most common objective in combinatorial optimization problems. However, such a single solution may not be applicable to real-world problems as objective functions and constraints are only…
Constraint satisfaction problems (CSPs) consist of a set of variables taking values from some finite domain and a set of local constraints on these variables. The objective is to find an assignment to the variables that maximizes the…
Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…