Related papers: Constraint Optimization and Statistical Mechanics
This paper deals with shape optimization for elastic materials under stochastic loads. It transfers the paradigm of stochastic dominance, which allows for flexible risk aversion via comparison with benchmark random variables, from…
Choosing decision variables deterministically (deterministic decision-making) can be regarded as a particular case of choosing decision variables probabilistically (probabilistic decision-making). It is necessary to investigate whether…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
We present a powerful general framework for designing data-dependent optimization algorithms, building upon and unifying recent techniques in adaptive regularization, optimistic gradient predictions, and problem-dependent randomization. We…
Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…
The graph coloring problem is a classical combinatorial optimization problem with important applications such as register allocation and task scheduling, and it has been extensively studied for decades. However, near-real-time algorithms…
The approximate graph colouring problem, whose complexity is unresolved in most cases, concerns finding a $c$-colouring of a graph that is promised to be $k$-colourable, where $c\geq k$. This problem naturally generalises to promise graph…
This work addresses the problem of predicting the motion trajectories of dynamic objects in the environment. Recent advances in predicting motion patterns often rely on machine learning techniques to extrapolate motion patterns from…
A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…
We discuss an analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring, in terms of an effective energy landscape. Several intriguing geometrical properties of the solution space become in this light…
This paper studies the optimization of observation channels (stochastic kernels) in partially observed stochastic control problems. In particular, existence and continuity properties are investigated mostly (but not exclusively)…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…
Network optimization has generally been focused on solving network flow problems, but recently there have been investigations into optimizing network characteristics. Optimizing network connectivity to maximize the number of nodes within a…
This is a review paper, summarizing without proofs recent results by the authors on the property of strong metric subregularity (SMSR) in optimization. It presents sufficient conditions for SMSR of the optimality mapping associated with a…
Quadratic programming (QP) is a common and important constrained optimization problem. Here, we derive a surprising duality between constrained optimization with inequality constraints -- of which QP is a special case -- and consumer…
Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to…
Mesoscopic systems in a slowly fluctuating environment are often well described by superstatistical models. We develop a generalized statistical mechanics formalism for superstatistical systems, by mapping the superstatistical complex…
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We…
Min-max optimization problems, also known as saddle point problems, have attracted significant attention due to their applications in various fields, such as fair beamforming, generative adversarial networks (GANs), and adversarial…