Võ Tiến Phát - Academia.edu (original) (raw)

Papers by Võ Tiến Phát

Siam Journal on Optimization, Jun 23, 2023

Mathematics of Operations Research, Dec 22, 2022

This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions ... more This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions defined by subgradients of extended-real-valued prox-regular functions. The proposed algorithm is formulated in terms of the second-order subdifferential of such functions that enjoys extensive calculus rules and can be efficiently computed for broad classes of extended-real-valued functions. Based on this and on metric regularity and subregularity properties of subgradient mappings, we establish verifiable conditions ensuring well-posedness of the proposed algorithm and its local superlinear convergence. The obtained results are also new for the class of equations defined by continuously differentiable functions with Lipschitzian gradients (C 1,1 functions), which is the underlying case of our consideration. The developed algorithms for prox-regular functions and its extension to a structured class of composite functions are formulated in terms of proximal mappings and forward-backward envelopes. Besides numerous illustrative examples and comparison with known algorithms for C 1,1 functions and generalized equations, the paper presents applications of the proposed algorithms to regularized least square problems arising in statistics, machine learning, and related disciplines

arXiv (Cornell University), Dec 13, 2022

This paper addresses the study and characterizations of variational convexity of extendedreal-val... more This paper addresses the study and characterizations of variational convexity of extendedreal-valued functions on Banach spaces. This notion has been recently introduced by Rockafellar, and its importance has been already realized and applied to continuous optimization problems in finitedimensional spaces. Variational convexity in infinite-dimensional spaces, which is studied here for the first time, is significantly more involved and requires the usage of powerful tools of geometric functional analysis together with variational analysis and generalized differentiation in Banach spaces.

SIAM Journal on Optimization

Mathematical Programming

This paper proposes and justifies two new globally convergent Newton-type methods to solve uncons... more This paper proposes and justifies two new globally convergent Newton-type methods to solve unconstrained and constrained problems of nonsmooth optimization by using tools of variational analysis and generalized differentiation. Both methods are coderivative-based and employ generalized Hessians (coderivatives of subgradient mappings) associated with objective functions, which are either of class C 1,1 , or are represented in the form of convex composite optimization, where one of the terms may be extended-real-valued. The proposed globally convergent algorithms are of two types. The first one extends the damped Newton method and requires positive-definiteness of the generalized Hessians for its well-posedness and efficient performance, while the other algorithm is of the Levenberg-Marquardt type being well-defined when the generalized Hessians are merely positive-semidefinite. The obtained convergence rates for both methods are at least linear, but becomes superlinear under the so-called semismooth * property of subgradient mappings. Problems of convex composite optimization are investigated with and without the strong convexity assumption on of smooth parts of objective functions by implementing the machinery of forward-backward envelopes. Numerical experiments are conducted for a basic class of Lasso problems by providing performance comparisons of the new algorithms with some other first-order and second-order methods that are highly recognized in nonsmooth optimization.

Mathematics of Operations Research

This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions ... more This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions defined by subgradients of extended real-valued prox-regular functions. The proposed algorithm is formulated in terms of the second order subdifferential of such functions that enjoy extensive calculus rules and can be efficiently computed for broad classes of extended real-valued functions. Based on this and on the metric regularity and subregularity properties of subgradient mappings, we establish verifiable conditions ensuring the well-posedness of the proposed algorithm and its local superlinear convergence. The obtained results are also new for the class of equations defined by continuously differentiable functions with Lipschitzian gradients ([Formula: see text] functions), which is the underlying case of our consideration. The developed algorithms for prox-regular functions and their extension to a structured class of composite functions are formulated in terms of proximal mapping...

Journal of Global Optimization

The paper proposes and develops new globally convergent algorithms of the generalized damped Newt... more The paper proposes and develops new globally convergent algorithms of the generalized damped Newton type for solving important classes of nonsmooth optimization problems. These algorithms are based on the theory and calculations of second-order subdifferentials of nonsmooth functions with employing the machinery of second-order variational analysis and generalized differentiation. First we develop a globally superlinearly convergent damped Newton-type algorithm for the class of continuously differentiable functions with Lipschitzian gradients, which are nonsmooth of second order. Then we design such a globally convergent algorithm to solve a structured class of nonsmooth quadratic composite problems with extended-real-valued cost functions, which typically arise in machine learning and statistics. Finally, we present the results of numerical experiments and compare the performance of our main algorithm applied to an important class of Lasso problems with those achieved by other first-order and second-order optimization algorithms.

arXiv (Cornell University), Oct 30, 2018

For a C 2-smooth function on a finite-dimensional space, a necessary condition for its quasiconve... more For a C 2-smooth function on a finite-dimensional space, a necessary condition for its quasiconvexity is the positive semidefiniteness of its Hessian matrix on the subspace orthogonal to its gradient, whereas a sufficient condition for its strict pseudoconvexity is the positive definiteness of its Hessian matrix on the subspace orthogonal to its gradient. Our aim in this paper is to extend those conditions for C 1,1-smooth functions by using the Fréchet and Mordukhovich second-order subdifferentials.

Biscuits, which are loved by many consumers, often provide a high level of energy because they ar... more Biscuits, which are loved by many consumers, often provide a high level of energy because they are rich in sugar, flour, fat and low in fiber. Fiber plays an important role in preventing constipation, cardiovascular diseases and obesity, so the current trend of manufacturers is to create high-fiber biscuit lines. Defatted copra meal (DCM) is a rich source of fiber and is added to biscuits to increase the fiber content of the cake. In this study, defatted copra meal, after being hydrolysed with the enzyme Cellulast1.5L (HDCM), will be used to replace wheat flour with different ratios, from 10% to 40%, in fiber rich biscuit recipe. The hydrolysis of DCM was carried out with an enzyme concentration of 5U/g dry matter, for 30 minutes. The obtained HDCM has a soluble fiber (SDF) content of 7.3% dry matter, an increase of 2.43 times compared to the DCM sample. At the same time, the ratio between insoluble fiber and soluble fiber (IDF/SDF) of HDCM also decreased by 2.64 times compared to t...

Optimization Letters, 2020

For a C 2-smooth function on a finite-dimensional space, a necessary condition for its quasiconve... more For a C 2-smooth function on a finite-dimensional space, a necessary condition for its quasiconvexity is the positive semidefiniteness of its Hessian matrix on the subspace orthogonal to its gradient, whereas a sufficient condition for its strict pseudoconvexity is the positive definiteness of its Hessian matrix on the subspace orthogonal to its gradient. Our aim in this paper is to extend those conditions for C 1,1-smooth functions by using the Fréchet and Mordukhovich second-order subdifferentials.

Operations Research Letters, 2018

Abstract This paper investigates the possibility of using the Frechet and Mordukhovich second-ord... more Abstract This paper investigates the possibility of using the Frechet and Mordukhovich second-order subdifferentials to characterize the robust quasiconvexity of C 1 -smooth functions. We set up a necessary condition for the robust quasiconvexity of C 1 , 1 -smooth functions and univariate C 1 -smooth ones. We also show that the established necessary condition is indeed a sufficient one for the robust quasiconvexity of C 1 -smooth functions.

Pediatric Nephrology, 2009

Sirs, I read with great interest the manuscript by Dr. Bockenhauer et al. describing a fatal case... more Sirs, I read with great interest the manuscript by Dr. Bockenhauer et al. describing a fatal case with cerebral edema and massive polyuria after kidney transplantation [1]. Polyuria after kidney transplantations is not a rare condition. This is especially due to an immature adaptation ...

Land Administration has been making a significant contribution to the socio-economic development ... more Land Administration has been making a significant contribution to the socio-economic development in Vietnam in recent decades. However, there are still many challenges for the reform process in this area. This paper presents two studies on the impact of Vietnam land policy to: 1) poverty alleviation - PEN II with case study at 6 provinces, 6 districts, 6 communes and 12 villages; and 2) Private sector development - this study provides an analysis on the feedback from the private sector after a year of implementatio n of the new land law. The feedback was collected from the Internet, newspapers, and questionnaire from business enterprises. The results of those studies: Improved Land use planning could have more impact on poverty alleviation at remote and upland areas. Land allocation is a good policy but it is still unclear regarding the impact on poor people in upland areas. For private sector development, land administration could continue the reform in administrativ e procedures f...

This paper presents an edge inference accelerator for deep learning application “Handwriting reco... more This paper presents an edge inference accelerator for deep learning application “Handwriting recognition” using field programmable gate array (FPGA). The parameter of the neuron network is trained using GPU and then download to an off-chip DRAM for the accelerator to access. The image data is transfered through Bluetooth from smart phone to the deep learning accelerator. This accelerator architecture can fit any neuron network and is suitable for consumer electronics such as IoT applications.

Siam Journal on Optimization, Jun 23, 2023

Mathematics of Operations Research, Dec 22, 2022

This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions ... more This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions defined by subgradients of extended-real-valued prox-regular functions. The proposed algorithm is formulated in terms of the second-order subdifferential of such functions that enjoys extensive calculus rules and can be efficiently computed for broad classes of extended-real-valued functions. Based on this and on metric regularity and subregularity properties of subgradient mappings, we establish verifiable conditions ensuring well-posedness of the proposed algorithm and its local superlinear convergence. The obtained results are also new for the class of equations defined by continuously differentiable functions with Lipschitzian gradients (C 1,1 functions), which is the underlying case of our consideration. The developed algorithms for prox-regular functions and its extension to a structured class of composite functions are formulated in terms of proximal mappings and forward-backward envelopes. Besides numerous illustrative examples and comparison with known algorithms for C 1,1 functions and generalized equations, the paper presents applications of the proposed algorithms to regularized least square problems arising in statistics, machine learning, and related disciplines

arXiv (Cornell University), Dec 13, 2022

This paper addresses the study and characterizations of variational convexity of extendedreal-val... more This paper addresses the study and characterizations of variational convexity of extendedreal-valued functions on Banach spaces. This notion has been recently introduced by Rockafellar, and its importance has been already realized and applied to continuous optimization problems in finitedimensional spaces. Variational convexity in infinite-dimensional spaces, which is studied here for the first time, is significantly more involved and requires the usage of powerful tools of geometric functional analysis together with variational analysis and generalized differentiation in Banach spaces.

SIAM Journal on Optimization

Mathematical Programming

This paper proposes and justifies two new globally convergent Newton-type methods to solve uncons... more This paper proposes and justifies two new globally convergent Newton-type methods to solve unconstrained and constrained problems of nonsmooth optimization by using tools of variational analysis and generalized differentiation. Both methods are coderivative-based and employ generalized Hessians (coderivatives of subgradient mappings) associated with objective functions, which are either of class C 1,1 , or are represented in the form of convex composite optimization, where one of the terms may be extended-real-valued. The proposed globally convergent algorithms are of two types. The first one extends the damped Newton method and requires positive-definiteness of the generalized Hessians for its well-posedness and efficient performance, while the other algorithm is of the Levenberg-Marquardt type being well-defined when the generalized Hessians are merely positive-semidefinite. The obtained convergence rates for both methods are at least linear, but becomes superlinear under the so-called semismooth * property of subgradient mappings. Problems of convex composite optimization are investigated with and without the strong convexity assumption on of smooth parts of objective functions by implementing the machinery of forward-backward envelopes. Numerical experiments are conducted for a basic class of Lasso problems by providing performance comparisons of the new algorithms with some other first-order and second-order methods that are highly recognized in nonsmooth optimization.

Mathematics of Operations Research

This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions ... more This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions defined by subgradients of extended real-valued prox-regular functions. The proposed algorithm is formulated in terms of the second order subdifferential of such functions that enjoy extensive calculus rules and can be efficiently computed for broad classes of extended real-valued functions. Based on this and on the metric regularity and subregularity properties of subgradient mappings, we establish verifiable conditions ensuring the well-posedness of the proposed algorithm and its local superlinear convergence. The obtained results are also new for the class of equations defined by continuously differentiable functions with Lipschitzian gradients ([Formula: see text] functions), which is the underlying case of our consideration. The developed algorithms for prox-regular functions and their extension to a structured class of composite functions are formulated in terms of proximal mapping...

Journal of Global Optimization

The paper proposes and develops new globally convergent algorithms of the generalized damped Newt... more The paper proposes and develops new globally convergent algorithms of the generalized damped Newton type for solving important classes of nonsmooth optimization problems. These algorithms are based on the theory and calculations of second-order subdifferentials of nonsmooth functions with employing the machinery of second-order variational analysis and generalized differentiation. First we develop a globally superlinearly convergent damped Newton-type algorithm for the class of continuously differentiable functions with Lipschitzian gradients, which are nonsmooth of second order. Then we design such a globally convergent algorithm to solve a structured class of nonsmooth quadratic composite problems with extended-real-valued cost functions, which typically arise in machine learning and statistics. Finally, we present the results of numerical experiments and compare the performance of our main algorithm applied to an important class of Lasso problems with those achieved by other first-order and second-order optimization algorithms.

arXiv (Cornell University), Oct 30, 2018

For a C 2-smooth function on a finite-dimensional space, a necessary condition for its quasiconve... more For a C 2-smooth function on a finite-dimensional space, a necessary condition for its quasiconvexity is the positive semidefiniteness of its Hessian matrix on the subspace orthogonal to its gradient, whereas a sufficient condition for its strict pseudoconvexity is the positive definiteness of its Hessian matrix on the subspace orthogonal to its gradient. Our aim in this paper is to extend those conditions for C 1,1-smooth functions by using the Fréchet and Mordukhovich second-order subdifferentials.

Biscuits, which are loved by many consumers, often provide a high level of energy because they ar... more Biscuits, which are loved by many consumers, often provide a high level of energy because they are rich in sugar, flour, fat and low in fiber. Fiber plays an important role in preventing constipation, cardiovascular diseases and obesity, so the current trend of manufacturers is to create high-fiber biscuit lines. Defatted copra meal (DCM) is a rich source of fiber and is added to biscuits to increase the fiber content of the cake. In this study, defatted copra meal, after being hydrolysed with the enzyme Cellulast1.5L (HDCM), will be used to replace wheat flour with different ratios, from 10% to 40%, in fiber rich biscuit recipe. The hydrolysis of DCM was carried out with an enzyme concentration of 5U/g dry matter, for 30 minutes. The obtained HDCM has a soluble fiber (SDF) content of 7.3% dry matter, an increase of 2.43 times compared to the DCM sample. At the same time, the ratio between insoluble fiber and soluble fiber (IDF/SDF) of HDCM also decreased by 2.64 times compared to t...

Optimization Letters, 2020

For a C 2-smooth function on a finite-dimensional space, a necessary condition for its quasiconve... more For a C 2-smooth function on a finite-dimensional space, a necessary condition for its quasiconvexity is the positive semidefiniteness of its Hessian matrix on the subspace orthogonal to its gradient, whereas a sufficient condition for its strict pseudoconvexity is the positive definiteness of its Hessian matrix on the subspace orthogonal to its gradient. Our aim in this paper is to extend those conditions for C 1,1-smooth functions by using the Fréchet and Mordukhovich second-order subdifferentials.

Operations Research Letters, 2018

Abstract This paper investigates the possibility of using the Frechet and Mordukhovich second-ord... more Abstract This paper investigates the possibility of using the Frechet and Mordukhovich second-order subdifferentials to characterize the robust quasiconvexity of C 1 -smooth functions. We set up a necessary condition for the robust quasiconvexity of C 1 , 1 -smooth functions and univariate C 1 -smooth ones. We also show that the established necessary condition is indeed a sufficient one for the robust quasiconvexity of C 1 -smooth functions.

Pediatric Nephrology, 2009

Sirs, I read with great interest the manuscript by Dr. Bockenhauer et al. describing a fatal case... more Sirs, I read with great interest the manuscript by Dr. Bockenhauer et al. describing a fatal case with cerebral edema and massive polyuria after kidney transplantation [1]. Polyuria after kidney transplantations is not a rare condition. This is especially due to an immature adaptation ...

Land Administration has been making a significant contribution to the socio-economic development ... more Land Administration has been making a significant contribution to the socio-economic development in Vietnam in recent decades. However, there are still many challenges for the reform process in this area. This paper presents two studies on the impact of Vietnam land policy to: 1) poverty alleviation - PEN II with case study at 6 provinces, 6 districts, 6 communes and 12 villages; and 2) Private sector development - this study provides an analysis on the feedback from the private sector after a year of implementatio n of the new land law. The feedback was collected from the Internet, newspapers, and questionnaire from business enterprises. The results of those studies: Improved Land use planning could have more impact on poverty alleviation at remote and upland areas. Land allocation is a good policy but it is still unclear regarding the impact on poor people in upland areas. For private sector development, land administration could continue the reform in administrativ e procedures f...

This paper presents an edge inference accelerator for deep learning application “Handwriting reco... more This paper presents an edge inference accelerator for deep learning application “Handwriting recognition” using field programmable gate array (FPGA). The parameter of the neuron network is trained using GPU and then download to an off-chip DRAM for the accelerator to access. The image data is transfered through Bluetooth from smart phone to the deep learning accelerator. This accelerator architecture can fit any neuron network and is suitable for consumer electronics such as IoT applications.