A strongly sub-feasible primal-dual quasi interior-point algorithm for nonlinear inequality constrained optimization

Jian, Jinbao; Pan, Hucheng; Tang, Chunming; Li, Jianling

doi:10.1016/j.amc.2015.05.091

Cited by 6 publications

(15 citation statements)

References 15 publications

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“…In this case, in view of dz k ∈ NS k , similar to [20], the results in the paper are shown to be still true. However, because the proposed algorithm is a penalty function type algorithm, the active set J k0 ∪ C F k0 ∪ C ψε k k0 is always very small.…”

Section: Global Convergencesupporting

confidence: 56%

A superlinearly convergent QP-free algorithm for mathematical programs with equilibrium constraints

Huang

Jian

2015

Applied Mathematics and Computation

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Section: Global Convergencesupporting

confidence: 56%

A superlinearly convergent QP-free algorithm for mathematical programs with equilibrium constraints

Huang

Jian

2015

Applied Mathematics and Computation

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“…In this paper, similarly to the techniques in [ 21 , 30 ], for the current iterate , we yield the corresponding multiplier vector in ( 3 )-( 4 ) as follows: where , and is computed in the previous iteration th. Then, similarly to [ 29 ], we structure our working set by The reason why one does not compute as is to force , see the analysis of Theorem 1 in Section 3 .…”

Section: Construction Of Algorithmmentioning

confidence: 99%

“…So, generally, the first direction should be corrected by another SLE. For this goal, refer to [ 21 ], we construct and solve in Step 3(iii), (iv). Lemma 2 and the global convergence analysis in the next section show that the algorithm with search direction is well defined and globally convergent.…”

Section: Construction Of Algorithmmentioning

confidence: 99%

“…More recently, for inequality constrained optimization, Jian et al [ 21 ] proposed a strongly sub-feasible primal-dual quasi interior-point algorithm with superlinear convergence, where the initial point can be chosen arbitrarily, the number of feasible constraints is nondecreasing, and the iteration points all enter into the interior of the feasible region after finite iterations; a new kind of working set was introduced, which further reduced the computational cost; the uniformly positive definite restriction on the sequence was relaxed; at each iteration, only two or three SLEs with the same coefficient matrix needed to be solved.…”

Section: Introductionmentioning

confidence: 99%

“…The goal of this paper is to improve and extend the algorithms [ 18 , 21 ] to nonlinear constrained optimization (P) and, at the same time, to overcome the three problems mentioned above. As a result, by means of problem (P ρ ), we propose a PDIP-type algorithm for problem (P).…”

Section: Introductionmentioning

confidence: 99%

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Primal-dual interior point QP-free algorithm for nonlinear constrained optimization

Jian

Zeng

et al. 2017

J Inequal Appl

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In this paper, a class of nonlinear constrained optimization problems with both inequality and equality constraints is discussed. Based on a simple and effective penalty parameter and the idea of primal-dual interior point methods, a QP-free algorithm for solving the discussed problems is presented. At each iteration, the algorithm needs to solve two or three reduced systems of linear equations with a common coefficient matrix, where a slightly new working set technique for judging the active set is used to construct the coefficient matrix, and the positive definiteness restriction on the Lagrangian Hessian estimate is relaxed. Under reasonable conditions, the proposed algorithm is globally and superlinearly convergent. During the numerical experiments, by modifying the technique in Section 5 of (SIAM J. Optim. 14(1): 173-199, 2003), we introduce a slightly new computation measure for the Lagrangian Hessian estimate based on second order derivative information, which can satisfy the associated assumptions. Then, the proposed algorithm is tested and compared on 59 typical test problems, which shows that the proposed algorithm is promising.

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Robust PID Control of EV Aggregator for C-FCAS Using Sequential Multi-Objective Optimization

Pradana,

Haque,

Krismanto

et al. 2024

IEEE Access

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Integrating Electric Vehicles (EVs) charging into power grids through EV aggregator, offers promising benefits to society for reliable, sustainable, and cost-effective energy solutions. A key aspect of this integration is the possibility of provision of Contingency-Frequency Control Ancillary Services (C-FCAS). While EVs primarily serve owners' transportation needs, they must return to their idle positions with a satisfactory State of Charge (SoC) after providing frequency support following a contingency. However, real-world implementations of grid-connected EV aggregator control for C-FCAS are complex and challenging because several factors, including uncertainties, perturbation magnitude, renewable energy penetration, and the SoC of EVs need to be considered. To implement the C-FCAS considering these factors, this paper presents a robust PID control approach for an EV aggregator. The objective is to effectively manage EV units willing to participate, ensuring frequency regulation support, system stability, and smooth return to their idle position. The strategy exploits a sequential multi-objective optimization approach with two main objectives: mitigating frequency perturbations caused by contingencies and restoring EV units power discharge to zero after a critical time period. Sequential Multi-objective Optimization (SMO) algorithms optimize the control parameters under diverse scenarios and uncertainties. The simulation results validate the effectiveness of the proposed strategy. The control strategy by an EV aggregator successfully handled different market conditions and uncertainties, ensuring reliable frequency regulation. This service opportunity will enhance income of EV owners and their willingness to participate while helping to keep the integrity of system operation.

show abstract

A strongly sub-feasible primal-dual quasi interior-point algorithm for nonlinear inequality constrained optimization

Cited by 6 publications

References 15 publications

A superlinearly convergent QP-free algorithm for mathematical programs with equilibrium constraints

A superlinearly convergent QP-free algorithm for mathematical programs with equilibrium constraints

Primal-dual interior point QP-free algorithm for nonlinear constrained optimization

Robust PID Control of EV Aggregator for C-FCAS Using Sequential Multi-Objective Optimization

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