An interior point technique for solving bilevel programming problems

Herskovits, José; Filho, Mario Tanaka; Leontiev, Anatoli

doi:10.1007/s11081-012-9192-4

Cited by 9 publications

(8 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where δ k > 0 is the radius of the trust-region. To evaluate the trial step d k , any approximation to the solution of the above Subproblem (12) can be used as long as a fraction of the Cauchy decrease condition holds. The fraction of the Cauchy decrease condition is the condition that a fraction of the predicted decrease obtained by the Cauchy step is less than or equal to the predicted decrease obtained by d k .…”

Section: Outline Of Pbtr Algorithmmentioning

confidence: 99%

“…The fraction of the Cauchy decrease condition is the condition that a fraction of the predicted decrease obtained by the Cauchy step is less than or equal to the predicted decrease obtained by d k . Therefore, a conjugate gradient method [35] is used to solve the Subproblem (12). In the following Algorithm 1, the main steps to solve Subproblem (12) are offered.…”

Section: Outline Of Pbtr Algorithmmentioning

confidence: 99%

“…Kebbiche et al [11] investigated a projective interior-point algorithm for solving general convex nonlinear problems. Herskovits et al [12] presented an interior-point-based approach for solving bilevel programming problems with convex lower-level problems. Zhang et al [13] presented an interior-point method-based program combined with the homogenization theory on micromechanics to analyze shakedown behavior at the macro-scale.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections

et al. 2021

View full text Add to dashboard Cite

In this paper, a penalty method is used together with a barrier method to transform a constrained nonlinear programming problem into an unconstrained nonlinear programming problem. In the proposed approach, Newton’s method is applied to the barrier Karush–Kuhn–Tucker conditions. To ensure global convergence from any starting point, a trust-region globalization strategy is used. A global convergence theory of the penalty–barrier trust-region (PBTR) algorithm is studied under four standard assumptions. The PBTR has new features; it is simpler, has rapid convergerce, and is easy to implement. Numerical simulation was performed on some benchmark problems. The proposed algorithm was implemented to find the optimal design of a canal section for minimum water loss for a triangle cross-section application. The results are promising when compared with well-known algorithms.

show abstract

Section: Outline Of Pbtr Algorithmmentioning

confidence: 99%

Section: Outline Of Pbtr Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections

et al. 2021

View full text Add to dashboard Cite

show abstract

“…Consequently, this problem is nonconvex. Therefore, there is no guarantee on the optimality of solution [15], and methods developed to solve nonlinear problems based on KKT conditions may face difficulties when directly applied to solve MPECs [39]. Nevertheless, algorithms and solution methods have been developed to deal with these difficulties [40][41][42][43][44][45][46].…”

Section: Mathematical Program With Equilibrium Constraints (Mpec)mentioning

confidence: 99%

Strategic bidding for price-maker producers in predominantly hydroelectric systems

Cruz¹,

Finardi

Matos³

et al. 2016

Electric Power Systems Research

View full text Add to dashboard Cite

“…Problem (1.1) has a wide range of applications in engineering; to have a flavour of this, see, e.g., [7] and references therein. One of the most common single-level transformation of problem (1.1) is the Karush-Kuhn-Tucker (KKT) reformulation, which consists of replacing inclusion y ∈ S(x) with the equivalent KKT conditions of the lower-level problem, under appropriate assumptions; see, e.g., [1,8,5,15,24]. As shown in [5], the first drawback of the KKT reformulation is that it is not necessarily equivalent to the original problem (1.1).…”

mentioning

confidence: 99%

Levenberg-Marquardt method and partial exact penalty parameter selection in bilevel optimization

Tin¹,

Zemkoho²

2021

Preprint

View full text Add to dashboard Cite

We consider the optimistic bilevel optimization problem, known to have a wide range of applications in engineering, that we transform into a single-level optimization problem by means of the lowerlevel optimal value function reformulation. Subsequently, based on the partial calmness concept, we build an equation system, which is parameterized by the corresponding partial exact penalization parameter. We then design and analyze a Levenberg-Marquardt method to solve this parametric system of equations. Considering the fact that the selection of the partial exact penalization parameter is a critical issue when numerically solving a bilevel optimization problem, we conduct a careful experimental study to this effect, in the context the Levenberg-Marquardt method, while using the Bilevel Optimization LIBrary (BOLIB) series of test problems.

show abstract

An interior point technique for solving bilevel programming problems

Cited by 9 publications

References 27 publications

Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections

Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections

Strategic bidding for price-maker producers in predominantly hydroelectric systems

Levenberg-Marquardt method and partial exact penalty parameter selection in bilevel optimization

Contact Info

Product

Resources

About