81,462 research outputs found
Generalized semi-infinite programming: Numerical aspects
Generalized semi-infinite optimization problems (GSIP) are considered. It is investigated how the numerical methods for standard semi-infinite programming (SIP) can be extended to GSIP. Newton methods can be extended immediately. For discretization methods the situation is more complicated. These difficulties are discussed and convergence results for a discretization and an exchange method are derived under fairly general assumptions. The question under which conditions GSIP represents a convex problem is answered
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
Design of nonuniform near allpass complementary FIR filters via a semi-infinite programming technique
In this paper, we consider the problem of designing a set of nonuniform near allpass complementary FIR filters. This problem can be formulated as a quadratic semi-infinite programming problem, where the objective is to minimize the sum of the ripple energy for the individual filters, subject to the passband and stopband specifications as well as to the allpass complementary specification. The dual parameterization method is used for solving the linear quadratic semi-infinite programming problem
Tangential Extremal Principles for Finite and Infinite Systems of Sets, II: Applications to Semi-infinite and Multiobjective Optimization
This paper contains selected applications of the new tangential extremal
principles and related results developed in Part I to calculus rules for
infinite intersections of sets and optimality conditions for problems of
semi-infinite programming and multiobjective optimization with countable
constraint
Constraint Qualifications and Optimality Conditions for Nonconvex Semi-Infinite and Infinite Programs
The paper concerns the study of new classes of nonlinear and nonconvex
optimization problems of the so-called infinite programming that are generally
defined on infinite-dimensional spaces of decision variables and contain
infinitely many of equality and inequality constraints with arbitrary (may not
be compact) index sets. These problems reduce to semi-infinite programs in the
case of finite-dimensional spaces of decision variables. We extend the
classical Mangasarian-Fromovitz and Farkas-Minkowski constraint qualifications
to such infinite and semi-infinite programs. The new qualification conditions
are used for efficient computing the appropriate normal cones to sets of
feasible solutions for these programs by employing advanced tools of
variational analysis and generalized differentiation. In the further
development we derive first-order necessary optimality conditions for infinite
and semi-infinite programs, which are new in both finite-dimensional and
infinite-dimensional settings.Comment: 28 page
Quantitative Stability and Optimality Conditions in Convex Semi-Infinite and Infinite Programming
This paper concerns parameterized convex infinite (or semi-infinite)
inequality systems whose decision variables run over general
infinite-dimensional Banach (resp. finite-dimensional) spaces and that are
indexed by an arbitrary fixed set T . Parameter perturbations on the right-hand
side of the inequalities are measurable and bounded, and thus the natural
parameter space is . Based on advanced variational analysis, we
derive a precise formula for computing the exact Lipschitzian bound of the
feasible solution map, which involves only the system data, and then show that
this exact bound agrees with the coderivative norm of the aforementioned
mapping. On one hand, in this way we extend to the convex setting the results
of [4] developed in the linear framework under the boundedness assumption on
the system coefficients. On the other hand, in the case when the decision space
is reflexive, we succeed to remove this boundedness assumption in the general
convex case, establishing therefore results new even for linear infinite and
semi-infinite systems. The last part of the paper provides verifiable necessary
optimality conditions for infinite and semi-infinite programs with convex
inequality constraints and general nonsmooth and nonconvex objectives. In this
way we extend the corresponding results of [5] obtained for programs with
linear infinite inequality constraints
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