Characterizing a Class of Robust Vector Polynomial Optimization via Sum of Squares Conditions

Sun, Xiang-Kai; Tan, Wen; Teo, Kok Lay

doi:10.1007/s10957-023-02184-6

Cited by 10 publications

(5 citation statements)

References 43 publications

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“…According to the system theory , NGD ( 6) and ( 11) are equivalent under the initial zero condition. The systematic representation for AGDs is helpful for implementing the reset scheme, and it will be shown that NGD (11) is more suitable for the reset scheme in the following.…”

Section: Systematic Representation For Agdsmentioning

confidence: 99%

“…The proposed reset scheme cannot be directly used for NGD (6) since y k is not the integral value of the control input and cannot be simply reset to zero when the reset condition holds. However, the reset scheme can be applied for its equivalent form (11), where part η z−λ can be viewed as the controller, part…”

Section: Reset Mgdmentioning

confidence: 99%

“…As the complexity of the problem increases rapidly, the problem of how to design high-efficiency optimization algorithms has gained increasing attention. To improve the performance of conventional GD, many variants such as GDs with additional momentum [7,8] and robust GDs [9][10][11] have been considered. Recently, it was found that control theories could contribute substantially to the analysis and design of high-efficiency GDs, and many important results have been reported.…”

Section: Introductionmentioning

confidence: 99%

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Improving the Performance of Optimization Algorithms Using the Adaptive Fixed-Time Scheme and Reset Scheme

Chen,

Sun,

Wang

2023

Mathematics

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Optimization algorithms have now played an important role in many fields, and the issue of how to design high-efficiency algorithms has gained increasing attention, for which it has been shown that advanced control theories could be helpful. In this paper, the fixed-time scheme and reset scheme are introduced to design high-efficiency gradient descent methods for unconstrained convex optimization problems. At first, a general reset framework for existing accelerated gradient descent methods is given based on the systematic representation, with which both convergence speed and stability are significantly improved. Then, the design of a novel adaptive fixed-time gradient descent, which has fewer tuning parameters and maintains better robustness to initial conditions, is presented. However, its discrete form introduces undesirable overshoot and easily leads to instability, and the reset scheme is then applied to overcome the drawbacks. The linear convergence and better stability of the proposed algorithms are theoretically proven, and several dedicated simulation examples are finally given to validate the effectiveness.

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Section: Systematic Representation For Agdsmentioning

confidence: 99%

Section: Reset Mgdmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Improving the Performance of Optimization Algorithms Using the Adaptive Fixed-Time Scheme and Reset Scheme

Chen,

Sun,

Wang

2023

Mathematics

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“…In addition, nonsmooth robustduality properties and -quasi saddle point theorems are also established. New results on optimality and duality results for uncertain multiobjective polynomial optimization problems are given in [22]. By using tangential subdifferential and robust optimization, Liu et al [23] obtained some characterizations of robust optimal solution sets for nonconvex uncertain semi-infinite optimization problems.…”

Section: Introductionmentioning

confidence: 99%

On Mond–Weir-Type Robust Duality for a Class of Uncertain Fractional Optimization Problems

Guo

2023

Axioms

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This article is focused on the investigation of Mond–Weir-type robust duality for a class of semi-infinite multi-objective fractional optimization with uncertainty in the constraint functions. We first establish a Mond–Weir-type robust dual problem for this fractional optimization problem. Then, by combining a new robust-type subdifferential constraint qualification condition and a generalized convex-inclusion assumption, we present robust ε-quasi-weak and strong duality properties between this uncertain fractional optimization and its uncertain Mond–Weir-type robust dual problem. Moreover, we also investigate robust ε-quasi converse-like duality properties between them.

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“…They include the bridge location problem, the design centering problem [7], the packing problem [8], the production-transportation planning problem [9], the location planning problem [10], the edge detection problem [11], the conic programming problem [12], cluster analysis [13], and regression analysis [14]. Recently, DC optimization problems with uncertain data has become an interesting topic, and the results from robust optimization, in particular those obtained in [15][16][17], can be extended to robust DC optimization.…”

Section: Introductionmentioning

confidence: 99%

Bundle Enrichment Method for Nonsmooth Difference of Convex Programming Problems

Gaudioso,

Taheri,

Bagirov

et al. 2023

Algorithms

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The Bundle Enrichment Method (BEM-DC) is introduced for solving nonsmooth difference of convex (DC) programming problems. The novelty of the method consists of the dynamic management of the bundle. More specifically, a DC model, being the difference of two convex piecewise affine functions, is formulated. The (global) minimization of the model is tackled by solving a set of convex problems whose cardinality depends on the number of linearizations adopted to approximate the second DC component function. The new bundle management policy distributes the information coming from previous iterations to separately model the DC components of the objective function. Such a distribution is driven by the sign of linearization errors. If the displacement suggested by the model minimization provides no sufficient decrease of the objective function, then the temporary enrichment of the cutting plane approximation of just the first DC component function takes place until either the termination of the algorithm is certified or a sufficient decrease is achieved. The convergence of the BEM-DC method is studied, and computational results on a set of academic test problems with nonsmooth DC objective functions are provided.

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Characterizing a Class of Robust Vector Polynomial Optimization via Sum of Squares Conditions

Cited by 10 publications

References 43 publications

Improving the Performance of Optimization Algorithms Using the Adaptive Fixed-Time Scheme and Reset Scheme

Improving the Performance of Optimization Algorithms Using the Adaptive Fixed-Time Scheme and Reset Scheme

On Mond–Weir-Type Robust Duality for a Class of Uncertain Fractional Optimization Problems

Bundle Enrichment Method for Nonsmooth Difference of Convex Programming Problems

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