Convex relaxations for global optimization under uncertainty described by continuous random variables
نویسندگان
چکیده
منابع مشابه
An Optimization Algorithm Inspired by the Phase Transition Phenomenon for Global Optimization Problems with Continuous Variables
In this paper, we propose a novel nature-inspired meta-heuristic algorithm for continuous global optimization, named the phase transition-based optimization algorithm (PTBO). It mimics three completely different kinds of motion characteristics of elements in three different phases, which are the unstable phase, the meta-stable phase, and the stable phase. Three corresponding operators, which ar...
متن کاملRandom Laplacian Matrices and Convex Relaxations
Abstract. The largest eigenvalue of a matrix is always larger or equal than its largest diagonal entry. We show that for a large class of random Laplacian matrices, this bound is essentially tight: the largest eigenvalue is, up to lower order terms, often the size of the largest diagonal entry. Besides being a simple tool to obtain precise estimates on the largest eigenvalue of a large class of...
متن کاملConvex relaxations of chance constrained optimization problems
In this paper we develop convex relaxations of chance constrained optimization problems in order to obtain lower bounds on the optimal value. Unlike existing statistical lower bounding techniques, our approach is designed to provide deterministic lower bounds. We show that a version of the proposed scheme leads to a tractable convex relaxation when the chance constraint function is affine with ...
متن کاملSimplified Copositive and Lagrangian Relaxations for Linearly Constrained Quadratic Optimization Problems in Continuous and Binary Variables
For a quadratic optimization problem (QOP) with linear equality constraints in continuous nonnegative variables and binary variables, we propose three relaxations in simplified forms with a parameter λ: Lagrangian, completely positive, and copositive relaxations. These relaxations are obtained by reducing the QOP to an equivalent QOP with a single quadratic equality constraint in nonnegative va...
متن کاملOn the approximability of adjustable robust convex optimization under uncertainty
In this paper, we consider adjustable robust versions of convex optimization problems with uncertain constraints and objectives and show that under fairly general assumptions, a static robust solution provides a good approximation for these adjustable robust problems. An adjustable robust optimization problem is usually intractable since it requires to compute a solution for all possible realiz...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: AIChE Journal
سال: 2018
ISSN: 0001-1541
DOI: 10.1002/aic.16064