Confidence structural robust optimization by non-linear semidefinite programming-based single-level formulation

2010 ◽  
Vol 86 (8) ◽  
pp. 953-974 ◽  
Author(s):  
Xu Guo ◽  
Jianming Du ◽  
Xixin Gao
Keyword(s):  
Robust Optimization ◽  
Semidefinite Programming ◽  
Single Level ◽  
Non Linear ◽  
Linear Semidefinite Programming

scholarly journals ON OPTIMUM DESIGN OF FRAME STRUCTURES

2020 ◽  
Vol 26 ◽  
pp. 117-125
Author(s):  
Marek Tyburec ◽  
Jan Zeman ◽  
Martin Kružík ◽  
Didier Henrion
Keyword(s):  
Semidefinite Programming ◽  
Optimization Problems ◽  
Polynomial Optimization ◽  
Optimality Criteria ◽  
Frame Structure ◽  
Frame Structures ◽  
Global Optimality ◽  
Solution Quality ◽  
Non Linear ◽  
Linear Semidefinite Programming

Optimization of frame structures is formulated as a non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii) optimality criteria method, (iii) non-linear semidefinite programming, and (iv) polynomial optimization. We show that polynomial optimization solves the frame structure optimization to global optimality by building the (moment-sums-of-squares) hierarchy of convex linear semidefinite programming problems, and it also provides guaranteed lower and upper bounds on optimal design. Finally, we solve three sample optimization problems and conclude that the local optimization approaches may indeed converge to local optima, without any solution quality measure, or even to infeasible points. These issues are readily overcome by using polynomial optimization, which exhibits a finite convergence, at the prize of higher computational demands.

Robust optimization of the non-linear behaviour of a vibrating system

2009 ◽  
Vol 28 (1) ◽  
pp. 141-154 ◽  
Author(s):  
M.-L. Bouazizi ◽  
S. Ghanmi ◽  
R. Nasri ◽  
N. Bouhaddi
Keyword(s):  
Robust Optimization ◽  
Vibrating System ◽  
Non Linear ◽  
Linear Behaviour

Robust optimization for non-linear impact of data variation

2018 ◽  
Vol 99 ◽  
pp. 38-47 ◽  
Author(s):  
Laurent Alfandari ◽  
Juan-Carlos Espinoza García
Keyword(s):  
Robust Optimization ◽  
Non Linear ◽  
Data Variation

Robust Optimization for Models with Uncertain Second-Order Cone and Semidefinite Programming Constraints

2021 ◽  
Author(s):  
Jianzhe Zhen ◽  
Frans J. C. T. de Ruiter ◽  
Ernst Roos ◽  
Dick den Hertog
Keyword(s):  
Robust Optimization ◽  
Semidefinite Programming ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Decision Rules ◽  
Second Order ◽  
Minimum Volume ◽  
Second Order Cone ◽  
Linear Decision Rules ◽  
Effectiveness And Efficiency

In this paper, we consider uncertain second-order cone (SOC) and semidefinite programming (SDP) constraints with polyhedral uncertainty, which are in general computationally intractable. We propose to reformulate an uncertain SOC or SDP constraint as a set of adjustable robust linear optimization constraints with an ellipsoidal or semidefinite representable uncertainty set, respectively. The resulting adjustable problem can then (approximately) be solved by using adjustable robust linear optimization techniques. For example, we show that if linear decision rules are used, then the final robust counterpart consists of SOC or SDP constraints, respectively, which have the same computational complexity as the nominal version of the original constraints. We propose an efficient method to obtain good lower bounds. Moreover, we extend our approach to other classes of robust optimization problems, such as nonlinear problems that contain wait-and-see variables, linear problems that contain bilinear uncertainty, and general conic constraints. Numerically, we apply our approach to reformulate the problem on finding the minimum volume circumscribing ellipsoid of a polytope and solve the resulting reformulation with linear and quadratic decision rules as well as Fourier-Motzkin elimination. We demonstrate the effectiveness and efficiency of the proposed approach by comparing it with the state-of-the-art copositive approach. Moreover, we apply the proposed approach to a robust regression problem and a robust sensor network problem and use linear decision rules to solve the resulting adjustable robust linear optimization problems, which solve the problem to (near) optimality. Summary of Contribution: Computing robust solutions for nonlinear optimization problems with uncertain second-order cone and semidefinite programming constraints are of much interest in real-life applications, yet they are in general computationally intractable. This paper proposes a computationally tractable approximation for such problems. Extensive computational experiments on (i) computing the minimum volume circumscribing ellipsoid of a polytope, (ii) robust regressions, and (iii) robust sensor networks are conducted to demonstrate the effectiveness and efficiency of the proposed approach.

A Sequential Convex Program Approach to an Inverse Linear Semidefinite Programming Problem

2016 ◽  
Vol 33 (04) ◽  
pp. 1650025 ◽  
Author(s):  
Jia Wu ◽  
Yi Zhang ◽  
Liwei Zhang ◽  
Yue Lu
Keyword(s):  
Semidefinite Programming ◽  
Programming Problem ◽  
Difficult Problem ◽  
Dc Programming ◽  
Convex Program ◽  
Objective Parameter ◽  
Program Approach ◽  
Semidefinite Programming Problem ◽  
The Right ◽  
Linear Semidefinite Programming

This paper is devoted to the study of solving method for a type of inverse linear semidefinite programming problem in which both the objective parameter and the right-hand side parameter of the linear semidefinite programs are required to adjust. Since such kind of inverse problem is equivalent to a mathematical program with semidefinite cone complementarity constraints which is a rather difficult problem, we reformulate it as a nonconvex semi-definte programming problem by introducing a nonsmooth partial penalty function to penalize the complementarity constraint. The penalized problem is actually a nonsmooth DC programming problem which can be solved by a sequential convex program approach. Convergence analysis of the penalty models and the sequential convex program approach are shown. Numerical results are reported to demonstrate the efficiency of our approach.

Sign in / Sign up

Export Citation Format

Share Document