Related papers: Optimization and benchmarking of the thermal cycli…
Computing an optimal cycle in a given homology class, also referred to as the homology localization problem, is known to be an NP-hard problem in general. Furthermore, there is currently no known optimality criterion that localizes classes…
Topology optimization problems often support multiple local minima due to a lack of convexity. Typically, gradient-based techniques combined with continuation in model parameters are used to promote convergence to more optimal solutions;…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
We derive several numerical methods for designing optimized first-order algorithms in unconstrained convex optimization settings. Our methods are based on the Performance Estimation Problem (PEP) framework, which casts the worst-case…
A procedure is presented which considerably improves the performance of local search based heuristic algorithms for combinatorial optimization problems. It increases the average `gain' of the individual local searches by merging pairs of…
This thesis is devoted to studying two tasks: refrigeration and the creation of correlations. In the refrigeration part, two different paradigms of cooling, namely coherent and incoherent, are defined. The connection that these paradigms…
We construct a convergent family of outer approximations for the problem of optimizing polynomial functions over convex bodies subject to polynomial constraints. This is achieved by generalizing the polarization hierarchy, which has…
A solid system consisting of two heat conducting cylinders with a thermoelectric converter (Peltier element) between them is considered. A nonlinear model, which was previously verified by authors, is used to design a constrained control…
Theoretical design of global optimization algorithms can profitably utilize recent statistical mechanical treatments of potential energy surfaces (PES's). Here we analyze a particular method to explain its success in locating global minima…
Selecting the best hyperparameters for a particular optimization instance, such as the learning rate and momentum, is an important but nonconvex problem. As a result, iterative optimization methods such as hypergradient descent lack global…
We describe a seriation algorithm for ranking a set of items given pairwise comparisons between these items. Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others. It does so by constructing a…
Nonconvex optimization problems arise in many areas of computational science and engineering and are (approximately) solved by a variety of algorithms. Existing algorithms usually only have local convergence or subsequence convergence of…
We propose and analyse primal-dual interior-point algorithms for convex optimization problems in conic form. The families of algorithms we analyse are so-called short-step algorithms and they match the current best iteration complexity…
We introduce a new workflow for unconstrained optimization whereby objective functions are mapped onto a physical domain to more easily design algorithms that are robust to hyperparameters and achieve fast convergence rates. Specifically,…
We consider decision problems of rating alternatives based on their pairwise comparisons according to two criteria. Given pairwise comparison matrices for each criterion, the problem is to find the overall scores of the alternatives. We…
In this article a topology optimization method is developed, which is aware of material uncertainties. The uncertainties are handled in a worst-case sense, i.e. the worst possible material distribution over a given uncertainty set is taken…
We propose a novel, flexible algorithm for combining together metaheuristicoptimizers for non-convex optimization problems. Our approach treatsthe constituent optimizers as a team of complex agents that communicateinformation amongst each…
Nonconvex trajectory optimization is at the core of designing trajectories for complex autonomous systems. A challenge for nonconvex trajectory optimization methods, such as sequential convex programming, is to find an effective…
In this work, the artificial recirculation of water is presented and analyzed, from the perspective of the optimal control of partial differential equations, as a tool to prevent eutrophication effects in large waterbodies. A novel…
Recommender system has been researched for decades with millions of different versions of algorithms created in the industry. In spite of the huge amount of work spent on the field, there are many basic questions to be answered in the…