Related papers: Minimum Entropy Combinatorial Optimization Problem…
The optimization of expensive-to-evaluate black-box functions over combinatorial structures is an ubiquitous task in machine learning, engineering and the natural sciences. The combinatorial explosion of the search space and costly…
We study output-sensitive algorithms and complexity for multiobjective combinatorial optimization problems. In this computational complexity framework, an algorithm for a general enumeration problem is regarded efficient if it is…
In this paper the approach to solving several combinatorial optimization problems using the local search and the genetic algorithm techniques is proposed. Initially this approach was developed in purpose to overcome some difficulties…
This paper establishes a strict mathematical relationship between an arbitrary continuous function on a compact set and its global minima, like the well-known first order optimality condition for convex and differentiable functions. By…
In this paper, we analyze the convergence of several discretize-then-optimize algorithms, based on either a second-order or a fourth-order finite difference discretization, for solving elliptic PDE-constrained optimization or optimal…
The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…
In this paper a class of combinatorial optimization problems with uncertain costs is discussed. The uncertainty is modeled by specifying a discrete scenario set containing $K$ distinct cost scenarios. The Ordered Weighted Averaging (OWA for…
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…
Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…
The paper addresses a new class of combinatorial problems which consist in restructuring of solutions (as structures) in combinatorial optimization. Two main features of the restructuring process are examined: (i) a cost of the…
Many systems exhibit a mixture of continuous and discrete dynamics. We consider a family of mixed-integer non-convex non-linear optimisation problems obtained in discretisations of optimal control of such systems. For this family, a…
In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…
In this paper, we propose an original approach to stochastic control problems. We consider a weak formulation that is written as an optimization (minimization) problem on the space of probability measures. We then introduce a penalized…
The purpose of the paper is to give a complete characterization of the continuity of lower envelopes in the infinite dimensional spaces in terms of the notion of c-regularity. As an application we introduce a variational unconstrained…
This paper discusses a class of combinatorial optimization problems with uncertain costs in the objective function. It is assumed that a sample of the cost realizations is available, which defines an empirical probability distribution for…
Stochastic optimization of continuous objectives is at the heart of modern machine learning. However, many important problems are of discrete nature and often involve submodular objectives. We seek to unleash the power of stochastic…
One of the most important combinatorial optimization problems is graph coloring. There are several variations of this problem involving additional constraints either on vertices or edges. They constitute models for real applications, such…
One of the most ubiquitous problems in optimization is that of finding all the elements of a finite set at which a function $f$ attains its minimum (or maximum). When the codomain of $f$ is equipped with a total order, it is easy to…
We consider a variant of the set covering problem with uncertain parameters, which we refer to as the chance-constrained set multicover problem (CC-SMCP). In this problem, we assume that there is uncertainty regarding whether a selected set…
We derive tight bounds on the expected weights of several combinatorial optimization problems for random point sets of size $n$ distributed among the leaves of a balanced hierarchically separated tree. We consider {\it monochromatic} and…