A standard branch-and-bound approach for nonlinear semi-infinite problems

Marendet, Antoine; Goldsztejn, Alexandre; Chabert, Gilles; Jermann, Christophe

doi:10.1016/j.ejor.2019.10.025

Cited by 12 publications

(4 citation statements)

References 47 publications

(103 reference statements)

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“…In the rare cases where the verification fails, the verification procedure proposed in [23] outputs a faulty frequency that can be added to the discretized set of frequencies for a new trial. Continuous variables generically lead to active constraints, which require some theory and accurate algorithms with some adaptive discretization to allow discovering active frequencies for optimal coefficients (see [22], [24] for details). Integer variables generically do not lead to active constraints.…”

Section: B Formulating Linear Frequency Constraintsmentioning

confidence: 99%

Hardware-aware Design of Multiplierless Second-Order IIR Filters with Minimum Adders

Garcia,

Volkova,

Kumm

et al. 2021

Preprint

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In this work we optimally solve the problem of multiplierless design of second-order Infinite Impulse Response filters with minimum number of adders. Given a frequency specification, we design a stable direct form filter with hardwareaware fixed-point coefficients that yielding minimal number of adders when replacing all the multiplications by bit shifts and additions. The coefficient design, quantization and implementation, typically conducted independently, are now gathered into one global optimization problem, modeled through integer linear programming and efficiently solved using generic solvers. We guarantee the frequency-domain specifications and stability, which together with optimal number of adders will significantly simplify design-space exploration for filter designers.The optimal filters are implemented within the FloPoCo IP core generator and synthesized for Field Programmable Gate Arrays. With respect to state-of-the-art three-step filter design methods, our one-step design approach achieves, on average, 42% reduction in number of lookup tables and 21% improvement in delay.

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Section: B Formulating Linear Frequency Constraintsmentioning

confidence: 99%

Hardware-aware Design of Multiplierless Second-Order IIR Filters with Minimum Adders

Garcia,

Volkova,

Kumm

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Am considers a nonlinear semi-in nite problem with at least one semiin nite constraint (SIC). Standard branch-and-bound algorithms adapt to such problems by extending the usual upper and lower-bound techniques for nonlinear inequality constraints to SIC [2]. Yongmoon presents a globally optimal algorithm for determining the rotational offsets between the rigidly coupled rotation sensor and the camera coordinate system.…”

Section: Introductionmentioning

confidence: 99%

Prediction of Phase-Controlled Breaking Zero Point of Electronic and Electrical Fault Current considering Branch Definition Algorithm

Li¹

2022

Mobile Information Systems

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Phase-control technology, which is also called simultaneous interconnection technology, is one of the latest developments in intelligent interconnection. With the subsequent development of the short-circuit system, which increased significantly, the switching capacity of the switch is tested. Applying arc power to the contact holes during a short circuit also causes extensive damage to the switch contacts, which severely affects the operation and life of the switch. To solve this problem, this paper introduces the branch definition algorithm, describes different types of faults occurring in power systems, proposes a general scheme for fault current phase-controlled breaking, derives a fault occurrence detection method and a phase control method, and performs a simulation analysis of the proposed branch definition algorithm; a single-phase short-circuit current model is built; and the algorithm is tested using simulation data. The oscilloscope acquisition data were simulated and analyzed to obtain the characteristic parameters of the waveform, and the online simulation results obtained were analyzed with the oscilloscope data. The experimental results show that the system designed in this paper can accurately predict the zero value, and the zero values obtained from four experiments conducted are 34.52 ms, 34.46 ms, 29.9 ms, and 29.84 ms, respectively.

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“…This generates infeasible iterates giving rigorous lower bounds to the optimal objective value. Recently, a branch-and-bound algorithm for the solution of SIP problems with a box-constrained lower level was proposed in [28]. In [13,39], a convexification method is proposed which adaptively constructs convex relaxations of the lower-level problem, replaces the relaxed lower-level problems equivalently by their KKT conditions, and solves the resulting mathematical restrictions with complementarity constraints.…”

Section: Introduction a Semi-infinite Programming (Sip) Problem Is An...mentioning

confidence: 99%

Convergent Algorithms for a Class of Convex Semi-infinite Programs

Cerulli¹,

Oustry²,

d'Ambrosio³

et al. 2022

SIAM J. Optim.

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We focus on convex semi-infinite programs with an infinite number of quadratically parametrized constraints. In our setting, the lower-level problem, i.e., the problem of finding the constraint that is the most violated by a given point, is not necessarily convex. We propose a new convergent approach to solve these semiinfinite programs. Based on the Lagrangian dual of the lower-level problem, we derive a convex and tractable restriction of the considered semi-infinite programming problem. We state sufficient conditions for the optimality of this restriction. If these conditions are not met, the restriction is enlarged through an Inner-Outer Approximation Algorithm, and its value converges to the value of the original semi-infinite problem. This new algorithmic approach is compared with the classical Cutting Plane algorithm. We also propose a new rate of convergence of the Cutting Plane algorithm, directly related to the iteration index, derived when the objective function is strongly convex, and under a strict feasibility assumption. We successfully test the two methods on two applications: the constrained quadratic regression and a zero-sum game with cubic payoff. Our results are compared to those obtained using the approach proposed in [29], as well as using the classical relaxation approach based on the KKT conditions of the lower-level problem.

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A standard branch-and-bound approach for nonlinear semi-infinite problems

Cited by 12 publications

References 47 publications

Hardware-aware Design of Multiplierless Second-Order IIR Filters with Minimum Adders

Hardware-aware Design of Multiplierless Second-Order IIR Filters with Minimum Adders

Prediction of Phase-Controlled Breaking Zero Point of Electronic and Electrical Fault Current considering Branch Definition Algorithm

Convergent Algorithms for a Class of Convex Semi-infinite Programs

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