880 research outputs found
Sequential Convex Programming Methods for Solving Nonlinear Optimization Problems with DC constraints
This paper investigates the relation between sequential convex programming
(SCP) as, e.g., defined in [24] and DC (difference of two convex functions)
programming. We first present an SCP algorithm for solving nonlinear
optimization problems with DC constraints and prove its convergence. Then we
combine the proposed algorithm with a relaxation technique to handle
inconsistent linearizations. Numerical tests are performed to investigate the
behaviour of the class of algorithms.Comment: 18 pages, 1 figur
A UNIFIED INTERIOR POINT FRAMEWORK FOR OPTIMIZATION ALGORITHMS
Interior Point algorithms are optimization methods developed over the last three decades following the 1984 fundamental paper of Karmarkar. Over this period, IPM algorithms have had a profound impact on optimization theory as well as practice and have been successfully applied to many problems of business, engineering and science. Because of their operational simplicity and wide applicability, IPM algorithms are now playing an increasingly important role in computational optimization and operations research. This article provides unified interior point algorithms to optimization problems as well as comparing performances with classical algorithms. Keywords Interior Point methods, Optimization algorithms, Lagrangian Multipliers,  Barrier methods, Newton’s method, Matrix-free method
Projection methods in conic optimization
There exist efficient algorithms to project a point onto the intersection of
a convex cone and an affine subspace. Those conic projections are in turn the
work-horse of a range of algorithms in conic optimization, having a variety of
applications in science, finance and engineering. This chapter reviews some of
these algorithms, emphasizing the so-called regularization algorithms for
linear conic optimization, and applications in polynomial optimization. This is
a presentation of the material of several recent research articles; we aim here
at clarifying the ideas, presenting them in a general framework, and pointing
out important techniques
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