9 research outputs found
Semidefinite relaxations for semi-infinite polynomial programming
This paper studies how to solve semi-infinite polynomial programming (SIPP)
problems by semidefinite relaxation method. We first introduce two SDP
relaxation methods for solving polynomial optimization problems with finitely
many constraints. Then we propose an exchange algorithm with SDP relaxations to
solve SIPP problems with compact index set. At last, we extend the proposed
method to SIPP problems with noncompact index set via homogenization. Numerical
results show that the algorithm is efficient in practice.Comment: 23 pages, 4 figure
An SDP method for Fractional Semi-infinite Programming Problems with SOS-convex polynomials
In this paper, we study a class of fractional semi-infinite polynomial
programming problems involving s.o.s-convex polynomial functions. For such a
problem, by a conic reformulation proposed in our previous work and the
quadratic modules associated with the index set, a hierarchy of semidefinite
programming (SDP) relaxations can be constructed and convergent upper bounds of
the optimum can be obtained. In this paper, by introducing Lasserre's
measure-based representation of nonnegative polynomials on the index set to the
conic reformulation, we present a new SDP relaxation method for the considered
problem. This method enables us to compute convergent lower bounds of the
optimum and extract approximate minimizers. Moreover, for a set defined by
infinitely many s.o.s-convex polynomial inequalities, we obtain a procedure to
construct a convergent sequence of outer approximations which have semidefinite
representations. The convergence rate of the lower bounds and outer
approximations are also discussed
Existence theorem and optimality conditions for a class of convex
The paper is devoted to study of a special class of semi-infinite problems arising in nonlinear parametric
optimization. These semi-infinite problems are convex and possess noncompact index sets. In the paper, we present
conditions, which guarantee the existence of optimal solutions, and prove new optimality criterion. An example illustrating
the obtained results is presented