This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this n...This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this notion characterizations of strict local minima of order k for a multiobjective optimization problem with a nonempty set constraint are established,generalizing the corresponding scalar case obtained by Studniarski[3].Also necessary not sufficient and sufficient not necessary optimality conditions for this minima are derived based on our directional derivatives,which are generalizations of some existing scalar results and equivalent to some existing multiobjective ones.Many examples are given to illustrate them there.展开更多
Sparse optimization has witnessed advancements in recent decades,and the step function finds extensive applications across various machine learning and signal processing domains.This paper integrates zero norm and the...Sparse optimization has witnessed advancements in recent decades,and the step function finds extensive applications across various machine learning and signal processing domains.This paper integrates zero norm and the step function to formulate a doublesparsity constrained optimization problem,wherein a linear equality constraint is also taken into consideration.By defining aτ-Lagrangian stationary point and a KKT point,we establish the first-order and second-order necessary and sufficient optimality conditions for the problem.Furthermore,we thoroughly elucidate their relationships to local and global optimal solutions.Finally,special cases and examples are presented to illustrate the obtained theorems.展开更多
Among steganalysis techniques,detection against MV(motion vector)domain-based video steganography in the HEVC(High Efficiency Video Coding)standard remains a challenging issue.For the purpose of improving the detectio...Among steganalysis techniques,detection against MV(motion vector)domain-based video steganography in the HEVC(High Efficiency Video Coding)standard remains a challenging issue.For the purpose of improving the detection performance,this paper proposes a steganalysis method that can perfectly detectMV-based steganography in HEVC.Firstly,we define the local optimality of MVP(Motion Vector Prediction)based on the technology of AMVP(Advanced Motion Vector Prediction).Secondly,we analyze that in HEVC video,message embedding either usingMVP index orMVD(Motion Vector Difference)may destroy the above optimality of MVP.And then,we define the optimal rate of MVP as a steganalysis feature.Finally,we conduct steganalysis detection experiments on two general datasets for three popular steganographymethods and compare the performance with four state-ofthe-art steganalysis methods.The experimental results demonstrate the effectiveness of the proposed feature set.Furthermore,our method stands out for its practical applicability,requiring no model training and exhibiting low computational complexity,making it a viable solution for real-world scenarios.展开更多
The conventional approach to optimizing tilt angles for fixed solar panels aims to maximize energy generation over the entire year. However, in the context of a supply controlled electric grid, where solar energy avai...The conventional approach to optimizing tilt angles for fixed solar panels aims to maximize energy generation over the entire year. However, in the context of a supply controlled electric grid, where solar energy availability varies, this criterion may not be optimal. This study explores two alternative optimization criteria focused on maximizing baseload supply potential and minimizing required storage capacity to address seasonality in energy generation. The optimal tilt angles determined for these criteria differed significantly from the standard approach. This research highlights additional factors crucial for designing solar power systems beyond gross energy generation, essential for the global transition towards a fully renewable energy-based electric grid in the future.展开更多
文摘This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this notion characterizations of strict local minima of order k for a multiobjective optimization problem with a nonempty set constraint are established,generalizing the corresponding scalar case obtained by Studniarski[3].Also necessary not sufficient and sufficient not necessary optimality conditions for this minima are derived based on our directional derivatives,which are generalizations of some existing scalar results and equivalent to some existing multiobjective ones.Many examples are given to illustrate them there.
基金Supported by the National Key R&D Program of China(No.2023YFA1011100)NSFC(No.12131004)。
文摘Sparse optimization has witnessed advancements in recent decades,and the step function finds extensive applications across various machine learning and signal processing domains.This paper integrates zero norm and the step function to formulate a doublesparsity constrained optimization problem,wherein a linear equality constraint is also taken into consideration.By defining aτ-Lagrangian stationary point and a KKT point,we establish the first-order and second-order necessary and sufficient optimality conditions for the problem.Furthermore,we thoroughly elucidate their relationships to local and global optimal solutions.Finally,special cases and examples are presented to illustrate the obtained theorems.
基金the National Natural Science Foundation of China(Grant Nos.62272478,62202496,61872384).
文摘Among steganalysis techniques,detection against MV(motion vector)domain-based video steganography in the HEVC(High Efficiency Video Coding)standard remains a challenging issue.For the purpose of improving the detection performance,this paper proposes a steganalysis method that can perfectly detectMV-based steganography in HEVC.Firstly,we define the local optimality of MVP(Motion Vector Prediction)based on the technology of AMVP(Advanced Motion Vector Prediction).Secondly,we analyze that in HEVC video,message embedding either usingMVP index orMVD(Motion Vector Difference)may destroy the above optimality of MVP.And then,we define the optimal rate of MVP as a steganalysis feature.Finally,we conduct steganalysis detection experiments on two general datasets for three popular steganographymethods and compare the performance with four state-ofthe-art steganalysis methods.The experimental results demonstrate the effectiveness of the proposed feature set.Furthermore,our method stands out for its practical applicability,requiring no model training and exhibiting low computational complexity,making it a viable solution for real-world scenarios.
文摘The conventional approach to optimizing tilt angles for fixed solar panels aims to maximize energy generation over the entire year. However, in the context of a supply controlled electric grid, where solar energy availability varies, this criterion may not be optimal. This study explores two alternative optimization criteria focused on maximizing baseload supply potential and minimizing required storage capacity to address seasonality in energy generation. The optimal tilt angles determined for these criteria differed significantly from the standard approach. This research highlights additional factors crucial for designing solar power systems beyond gross energy generation, essential for the global transition towards a fully renewable energy-based electric grid in the future.
