Related papers: Statistical Physics of Hard Optimization Problems
Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…
Interdiction problems ask about the worst-case impact of a limited change to an underlying optimization problem. They are a natural way to measure the robustness of a system, or to identify its weakest spots. Interdiction problems have been…
We consider a class of combinatorial optimization problems that emerge in a variety of domains among which: condensed matter physics, theory of financial risks, error correcting codes in information transmissions, molecular and protein…
Purpose: To describe and mathematically validate the superiorization methodology, which is a recently-developed heuristic approach to optimization, and to discuss its applicability to medical physics problem formulations that specify the…
We study constraint satisfaction problems on the so-called 'planted' random ensemble. We show that for a certain class of problems, e.g. graph coloring, many of the properties of the usual random ensemble are quantitatively identical in the…
We convert, within polynomial-time and sequential processing, an NP-Complete Problem into a real-variable problem of minimizing a sum of Rational Linear Functions constrained by an Asymptotic-Linear-Program. The coefficients and constants…
In this thesis I explore challenging discrete energy minimization problems that arise mainly in the context of computer vision tasks. This work motivates the use of such "hard-to-optimize" non-submodular functionals, and proposes methods…
A canonical feature of the constraint satisfaction problems in NP is approximation hardness, where in the worst case, finding sufficient-quality approximate solutions is exponentially hard for all known methods. Fundamentally, the lack of…
The adaptation of neural codes to the statistics of their environment is well captured by efficient coding approaches. Here we solve an inverse problem: characterizing the objective and constraint functions that efficient codes appear to be…
The set of solutions of random constraint satisfaction problems (zero energy groundstates of mean-field diluted spin glasses) undergoes several structural phase transitions as the amount of constraints is increased. This set first breaks…
Simulation Optimization (SO) refers to the optimization of an objective function subject to constraints, both of which can be evaluated through a stochastic simulation. To address specific features of a particular simulation---discrete or…
This thesis investigates the extent to which the optimal value of a constraint satisfaction problem (CSP) can be approximated by some sentence of fixed point logic with counting (FPC). It is known that, assuming $\mathsf{P} \neq…
We introduce the idea that the P vs NP problem can have a finer structure. Given the NP complete problem of interest, the configurations space of the problem can be divided in (at least) two regions. In one region, polynomial algorithms to…
Optimization problems constrained by partial differential equations (PDEs) naturally arise in scientific computing, as those constraints often model physical systems or the simulation thereof. In an implicitly constrained approach, the…
In this dissertation we study statistical and online learning problems from an optimization viewpoint.The dissertation is divided into two parts : I. We first consider the question of learnability for statistical learning problems in the…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…
Ordinary approach to quantum algorithm is based on quantum Turing machine or quantum circuits. It is known that this approach is not powerful enough to solve NP-complete problems. In this paper we study a new approach to quantum algorithm…
We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…
Symmetries occur naturally in CSP or SAT problems and are not very difficult to discover, but using them to prune the search space tends to be very challenging. Indeed, this usually requires finding specific elements in a group of…