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Numerical algebraic geometry and semidefinite programming
Results in Applied Mathematics, 2021 Standard interior point methods in semidefinite programming can be viewed as tracking a solution path for a homotopy defined by a system of bilinear equations.
Jonathan D. Hauenstein +3 more
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Exact Optimal Designs of Experiments for Factorial Models via Mixed-Integer Semidefinite Programming
Mathematics, 2023 The systematic design of exact optimal designs of experiments is typically challenging, as it results in nonconvex optimization problems. The literature on the computation of model-based exact optimal designs of experiments via mathematical programming ...
Belmiro P. M. Duarte
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Critical Multipliers in Semidefinite Programming [PDF]
Asia-Pacific Journal of Operational Research, 2020 It was proved in Izmailov and Solodov (2014). Newton-Type Methods for Optimization and Variational Problems, Springer] that the existence of a noncritical multiplier for a (smooth) nonlinear programming problem is equivalent to an error bound condition for the Karush–Kuhn–Thcker (KKT) system without any assumptions.
Tianyu Zhang, Liwei Zhang
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Enhancing pseudo-telepathy in the magic square game. [PDF]
PLoS ONE, 2013 We study the possibility of reversing an action of a quantum channel. Our principal objective is to find a specific channel that reverses as accurately as possible an action of a given quantum channel. To achieve this goal we use semidefinite programming.
Lukasz Pawela +3 more
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Entropy-Penalized Semidefinite Programming [PDF]
Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, 2019 Low-rank methods for semi-definite programming (SDP) have gained a lot of interest recently, especially in machine learning applications. Their analysis often involves determinant-based or Schatten-norm penalties, which are difficult to implement in practice due to high computational efforts.
Mikhail Krechetov +3 more
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Reformulations of mathematical programming problems as linear complementarity problems [PDF]
, 1982 A family of complementarity problems are defined as extensions of the well known Linear Complementarity Problem (LCP). These are (i.) Second Linear Complementarity Problem (SLCP) which is an LCP extended by introducing further equality restrictions and ...
Mitra, G, Judice, JJ
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Open Journal of Mathematical Optimization, 2022 We address the issue of computing a global minimizer of the AC Optimal Power Flow problem. We introduce valid inequalities to strengthen the Semidefinite Programming relaxation, yielding a novel Conic Programming relaxation.
Oustry, Antoine
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A superlinearly convergent SSDP algorithm for nonlinear semidefinite programming
Journal of Inequalities and Applications, 2019 In this paper, we present a sequential semidefinite programming (SSDP) algorithm for nonlinear semidefinite programming. At each iteration, a linear semidefinite programming subproblem and a modified quadratic semidefinite programming subproblem are ...
Jian Ling Li, Hui Zhang
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Invariant Semidefinite Programs [PDF]
, 2011 In the last years many results in the area of semidefinite programming were obtained for invariant (finite dimensional, or infinite dimensional) semidefinite programs - SDPs which have symmetry. This was done for a variety of problems and applications. The purpose of this handbook chapter is to give the reader the necessary background for dealing with ...
C. Bachoc +3 more
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Quantum Goemans-Williamson Algorithm with the Hadamard Test and Approximate Amplitude Constraints [PDF]
Quantum, 2023 Semidefinite programs are optimization methods with a wide array of applications, such as approximating difficult combinatorial problems. One such semidefinite program is the Goemans-Williamson algorithm, a popular integer relaxation technique.
Taylor L. Patti +3 more
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