Multiplier Stabilization Applied to Two-Stage Stochastic Programs

Clara Lage (), Claudia Sagastizábal () and Mikhail Solodov ()
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Clara Lage: ENGIE
Claudia Sagastizábal: IMECC - UNICAMP
Mikhail Solodov: IMPA – Instituto de Matemática Pura e Aplicada

Journal of Optimization Theory and Applications, 2019, vol. 183, issue 1, No 9, 158-178

Abstract: Abstract In many mathematical optimization applications, dual variables are an important output of the solving process, due to their role as price signals. When dual solutions are not unique, different solvers or different computers, even different runs in the same computer if the problem is stochastic, often end up with different optimal multipliers. From the perspective of a decision maker, this variability makes the price signals less reliable and, hence, less useful. We address this issue for a particular family of linear and quadratic programs by proposing a solution procedure that, among all possible optimal multipliers, systematically yields the one with the smallest norm. The approach, based on penalization techniques of nonlinear programming, amounts to a regularization in the dual of the original problem. As the penalty parameter tends to zero, convergence of the primal sequence and, more critically, of the dual is shown under natural assumptions. The methodology is illustrated on a battery of two-stage stochastic linear programs.

Keywords: Multiplier stability; Dual regularization; Penalty method; Stochastic programming; Two-stage stochastic programming; Empirical approximations; 90C15; 65K05; 90C25; 65K10; 46N10 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-019-01550-7

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