20th EUROpt Workshop: Continuous Optimization Working Group is coming home
Corvinus University of Budapest

Plenary Speakers

Aharon Ben-Tal (Faculty of Data and Decision Sciences, Technion Israel Institute of Technology)

Title: An Algorithm for Maximizing a Convex Function Based on its Minimum, and Beyond

Abstract: In this talk the COMAX algorithm for maximizing a convex function over a convex feasible set (an NP-hard problem) is proposed. The algorithm consists of two phases: in phase 1 a feasible starting point is obtained that is used in a Gradient Descent algorithm in phase 2. The main contribution of the paper is connected to phase 1; five different methods are used to approximate the original NP-hard problem of maximizing a convex function (MCF) by a tractable convex optimization problem. All the methods use the minimizer of the convex objective function in their construction. The performance of the overall algorithm is tested on a wide variety of MCF problems, demonstrating its efficiency. As a next step COMAX is used in the design of new algorithms of optimizing a difference of convex functions.

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Coralia Cartis (Mathematical Institute, University of Oxford)

Title: Tensor methods for nonconvex optimization

Abstract: We consider the advantages of having and incorporating higher- (than second-) order derivative information inside regularization frameworks, generating higher-order regularization algorithms that have better complexity, universal properties and can certify higher-order criticality of candidate solutions. We discuss practical implementations of some of these methods, which involve the challenging solution of polynomial subproblems. Theoretical and numerical results for the latter will be presented.

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Russell Luke (Institute for Numerical and Applied Mathematics, University of Goettingen)

Title: Proximal Splitting Algorithms in Nonlinear Spaces

Abstract: Motivated by the problem of computing Fr├ęchet means of points in spaces of phylogenetic trees, we examine proximal splitting algorithms in general uniformly convex spaces, possibly with positive curvature. Several key notions from linear space theory no longer apply in this setting and force a reconfiguration of regularity concepts that explicitly accounts for the regularity of the space in which the algorithms run. We present a few convergence results for proximal splitting algorithms that benefit from the analysis of these algorithms when applied to nonconvex problems in linear spaces.

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Renata Sotirov (Department of Econometrics & Operations Research, Tilburg School of Economics and Management, Tilburg University)

Title: Mixed-Integer Semidefinite Programming - a New Perspective

Abstract: Mixed-integer semidefinite programming can be viewed as a generalization of mixed-integer programming where the vector of variables is replaced by mixed-integer positive semidefinite matrix variables. The combination of positive semidefiniteness and integrality allows to formulate various nonlinear optimization problems as (linear) mixed-integer semidefinite programs (MISDPs). Although MISDPs appeared already in the last century, they received little attention until recently. In this talk we present new results on MISDPs and resulting continuous relaxations. Finally, we present novel approaches for solving MISDPs.

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