In this paper, we present a sequential semidefinite programming (SSDP) algorithm for nonlinear semidefiniteprogramming. At each iteration, a linear semidefiniteprogramming subproblem and a modified quadratic semidef...
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In this paper, we present a sequential semidefinite programming (SSDP) algorithm for nonlinear semidefiniteprogramming. At each iteration, a linear semidefiniteprogramming subproblem and a modified quadratic semidefiniteprogramming subproblem are solved to generate a master search direction. In order to avoid Maratos effect, a second-order correction direction is determined by solving a new quadratic programming. And then a penalty function is used as a merit function for arc search. The superlinear convergence is shown under the strict complementarity and the strong second-order sufficient conditions with the sigma term. Finally, some preliminary numerical results are reported.
This paper discusses nonlinear optimization techniques in robust control synthesis, with special emphasis on design problems which may be cast as minimizing a linear objective function under linear matrix inequality (...
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This paper discusses nonlinear optimization techniques in robust control synthesis, with special emphasis on design problems which may be cast as minimizing a linear objective function under linear matrix inequality (LMI) constraints in tandem with nonlinear matrix equality constraints. The latter type of constraints renders the design numerically and algorithmically difficult. We solve the optimization problem via sequential semidefinite programming (SSDP), a technique which expands on sequential quadratic programming (SQP) known in nonlinear optimization. Global and fast local convergence properties of SSDP are similar to those of SQP, and SSDP is conveniently implemented with available semidefiniteprogramming ( SDP) solvers. Using two test examples, we compare SSDP to the augmented Lagrangian method, another classical scheme in nonlinear optimization, and to an approach using concave optimization.
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