A Unifying Approach to Robust Convex Infinite Optimization Duality
نویسندگان
چکیده
منابع مشابه
A Semidefinite Optimization Approach to Quadratic Fractional Optimization with a Strictly Convex Quadratic Constraint
In this paper we consider a fractional optimization problem that minimizes the ratio of two quadratic functions subject to a strictly convex quadratic constraint. First using the extension of Charnes-Cooper transformation, an equivalent homogenized quadratic reformulation of the problem is given. Then we show that under certain assumptions, it can be solved to global optimality using semidefini...
متن کاملAn Introduction to Duality in Convex Optimization
ABSTRACT This paper provides a short introduction to the Lagrangian duality in convex optimization. At first the topic is motivated by outlining the importance of convex optimization. After that mathematical optimization classes such as convex, linear and non-convex optimization, are defined. Later the Lagrangian duality is introduced. Weak and strong duality are explained and optimality condit...
متن کاملProjection: A Unified Approach to Semi-Infinite Linear Programs and Duality in Convex Programming
Fourier-Motzkin elimination is a projection algorithm for solving finite linear programs. Weextend Fourier-Motzkin elimination to semi-infinite linear programs which are linear programswith finitely many variables and infinitely many constraints. Applying projection leads to newcharacterizations of important properties for primal-dual pairs of semi-infinite programs suchas zero ...
متن کاملConvex Optimization and Lagrangian Duality
Finally the Lagranage dual function is given by g(~λ, ~ν) = inf~x L(~x,~λ, ~ν) We now make a couple of simple observations. Observation. When L(·, ~λ, ~ν) is unbounded from below then the dual takes the value −∞. Observation. g(~λ, ~ν) is concave1 as it is the infimum of a set of affine2 functions. If x is feasible solution of program (10.2)(10.4), then we have the following L(x,~λ, ~ν) = f0(x)...
متن کاملA Cutting Surface Algorithm for Semi-Infinite Convex Programming with an Application to Moment Robust Optimization
We first present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems, and use it to develop an algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. The cutting surface algorithm is also applicable to problems with non-differentiable sem...
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: Journal of Optimization Theory and Applications
سال: 2017
ISSN: 0022-3239,1573-2878
DOI: 10.1007/s10957-017-1136-x