Pub Date : 2024-01-16DOI: 10.1080/10556788.2023.2296438
Vincent Acary, Paul Armand, Hoang Minh Nguyen, Maksym Shpakovych
,
,
{"title":"Second-order cone programming for frictional contact mechanics using interior point algorithm","authors":"Vincent Acary, Paul Armand, Hoang Minh Nguyen, Maksym Shpakovych","doi":"10.1080/10556788.2023.2296438","DOIUrl":"https://doi.org/10.1080/10556788.2023.2296438","url":null,"abstract":",","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"34 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139528474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-08DOI: 10.1080/10556788.2023.2246169
Bardhyl Miftari, M. Berger, Guillaume Derval, Q. Louveaux, Damien Ernst
{"title":"GBOML: a structure-exploiting optimization modelling language in Python","authors":"Bardhyl Miftari, M. Berger, Guillaume Derval, Q. Louveaux, Damien Ernst","doi":"10.1080/10556788.2023.2246169","DOIUrl":"https://doi.org/10.1080/10556788.2023.2246169","url":null,"abstract":"","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130035079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-31DOI: 10.1080/10556788.2023.2241154
Gwenaël Samain, S. Bourguignon, Jordan Ninin
{"title":"Techniques for accelerating branch-and-bound algorithms dedicated to sparse optimization","authors":"Gwenaël Samain, S. Bourguignon, Jordan Ninin","doi":"10.1080/10556788.2023.2241154","DOIUrl":"https://doi.org/10.1080/10556788.2023.2241154","url":null,"abstract":"","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117008438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-18DOI: 10.1080/10556788.2023.2241769
Michael W. Ferry, P. Gill, Elizabeth Wong, Minxin Zhang
Projected-search methods for bound-constrained optimization are based on performing a search along a piecewise-linear continuous path obtained by projecting a search direction onto the feasible region. A potential benefit of a projected-search method is that many changes to the active set can be made at the cost of computing a single search direction. As the objective function is not differentiable along the search path, it is not possible to use a projected-search method with a step that satisfies the Wolfe conditions, which require the directional derivative of the objective function at a point on the path. For this reason, methods based in full or in part on a simple backtracking procedure must be used to give a step that satisfies an “Armijo-like” sufficient decrease condition. As a consequence, conventional projected-search methods are unable to exploit sophisticated safeguarded polynomial interpolation techniques that have been shown to be effective for the unconstrained case. This paper describes a new framework for the development of a general class of projectedsearch methods for bound-constrained optimization. At each iteration, a descent direction is computed with respect to a certain extended active set. This direction is used to specify a search direction that is used in conjunction with a step length computed by a quasi-Wolfe search. The quasi-Wolfe search is designed specifically for use with a piecewise-linear search path and is similar to a conventional Wolfe line search, except that a step is accepted under a wider range of conditions. These conditions take into consideration steps at which the restriction of the objective function on the search path is not differentiable. Standard existence and convergence results associated with a conventional Wolfe line search are extended to the quasi-Wolfe case. In addition, it is shown that under a standard nondegeneracy assumption, any method within the framework will identify the optimal active set in a finite number of iterations. Computational results are given for a specific projected-search method that uses a limited-memory quasi-Newton approximation of the Hessian. The results show that, in this context, a quasi-Wolfe search is substantially more efficient and reliable than an Armijolike search based on simple backtracking. Comparisons with a state-of-the-art boundconstrained optimization package are also presented.
{"title":"A class of projected-search methods for bound-constrained optimization","authors":"Michael W. Ferry, P. Gill, Elizabeth Wong, Minxin Zhang","doi":"10.1080/10556788.2023.2241769","DOIUrl":"https://doi.org/10.1080/10556788.2023.2241769","url":null,"abstract":"Projected-search methods for bound-constrained optimization are based on performing a search along a piecewise-linear continuous path obtained by projecting a search direction onto the feasible region. A potential benefit of a projected-search method is that many changes to the active set can be made at the cost of computing a single search direction. As the objective function is not differentiable along the search path, it is not possible to use a projected-search method with a step that satisfies the Wolfe conditions, which require the directional derivative of the objective function at a point on the path. For this reason, methods based in full or in part on a simple backtracking procedure must be used to give a step that satisfies an “Armijo-like” sufficient decrease condition. As a consequence, conventional projected-search methods are unable to exploit sophisticated safeguarded polynomial interpolation techniques that have been shown to be effective for the unconstrained case. This paper describes a new framework for the development of a general class of projectedsearch methods for bound-constrained optimization. At each iteration, a descent direction is computed with respect to a certain extended active set. This direction is used to specify a search direction that is used in conjunction with a step length computed by a quasi-Wolfe search. The quasi-Wolfe search is designed specifically for use with a piecewise-linear search path and is similar to a conventional Wolfe line search, except that a step is accepted under a wider range of conditions. These conditions take into consideration steps at which the restriction of the objective function on the search path is not differentiable. Standard existence and convergence results associated with a conventional Wolfe line search are extended to the quasi-Wolfe case. In addition, it is shown that under a standard nondegeneracy assumption, any method within the framework will identify the optimal active set in a finite number of iterations. Computational results are given for a specific projected-search method that uses a limited-memory quasi-Newton approximation of the Hessian. The results show that, in this context, a quasi-Wolfe search is substantially more efficient and reliable than an Armijolike search based on simple backtracking. Comparisons with a state-of-the-art boundconstrained optimization package are also presented.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115395259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-15DOI: 10.1080/10556788.2023.2246168
C. Izuchukwu, Y. Shehu
{"title":"A new inertial projected reflected gradient method with application to optimal control problems","authors":"C. Izuchukwu, Y. Shehu","doi":"10.1080/10556788.2023.2246168","DOIUrl":"https://doi.org/10.1080/10556788.2023.2246168","url":null,"abstract":"","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133868801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-08DOI: 10.1080/10556788.2023.2241148
Mercedes Pelegrín, C. D’Ambrosio, R. Delmas, Youssef Hamadi
Urban Air Mobility (UAM) has the potential to revolutionize transportation. It will exploit the third dimension to help smooth ground traffic in densely populated areas. This new paradigm in mobility will require methods to ensure safety and maximize efficiency. We propose to use mathematical optimization to address tactical deconfliction in UAM. Our approach is envisioned as a way of modelling and solving tactical conflicts, but also as means for assessing future infrastructures with potential utility in the design phase. We leverage envisioned UAM corridors to provide a mathematical definition of vehicle separation. A mathematical formulation is then proposed, which minimizes the total deviation from flight schedules needed to avoid loss of pairwise separation. The deconfliction is based on both airborne adjustments (through speed changes) and ground delays (holds relative to the scheduled take-off). Our experimental setup includes three use cases standing for different sources of conflicts and three synthetic UAM network topologies, which represent heterogeneous realistic scenarios. Vehicle and network capabilities are represented through model parameters, which allows us to analyse their impact on the quality of the deconfliction. Finally, insightful comparisons between our approach and both a local deconfliction and a fairness-oriented version are provided.
{"title":"Urban air mobility: from complex tactical conflict resolution to network design and fairness insights","authors":"Mercedes Pelegrín, C. D’Ambrosio, R. Delmas, Youssef Hamadi","doi":"10.1080/10556788.2023.2241148","DOIUrl":"https://doi.org/10.1080/10556788.2023.2241148","url":null,"abstract":"Urban Air Mobility (UAM) has the potential to revolutionize transportation. It will exploit the third dimension to help smooth ground traffic in densely populated areas. This new paradigm in mobility will require methods to ensure safety and maximize efficiency. We propose to use mathematical optimization to address tactical deconfliction in UAM. Our approach is envisioned as a way of modelling and solving tactical conflicts, but also as means for assessing future infrastructures with potential utility in the design phase. We leverage envisioned UAM corridors to provide a mathematical definition of vehicle separation. A mathematical formulation is then proposed, which minimizes the total deviation from flight schedules needed to avoid loss of pairwise separation. The deconfliction is based on both airborne adjustments (through speed changes) and ground delays (holds relative to the scheduled take-off). Our experimental setup includes three use cases standing for different sources of conflicts and three synthetic UAM network topologies, which represent heterogeneous realistic scenarios. Vehicle and network capabilities are represented through model parameters, which allows us to analyse their impact on the quality of the deconfliction. Finally, insightful comparisons between our approach and both a local deconfliction and a fairness-oriented version are provided.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"47 75","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133323304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-08DOI: 10.1080/10556788.2023.2210253
S. Gratton, S. Jerad, P. Toint
This paper considers optimization of nonconvex functionals in smooth infinite dimensional spaces. It is first proved that functionals in a class containing multivariate polynomials augmented with a sufficiently smooth regularization can be minimized by a simple linesearch-based algorithm. Sufficient smoothness depends on gradients satisfying a novel two-terms generalized Lipschitz condition. A first-order adaptive regularization method applicable to functionals with β-Hölder continuous derivatives is then proposed, that uses the linesearch approach to compute a suitable trial step. It is shown to find an ϵ-approximate first-order point in at most evaluations of the functional and its first p derivatives.
{"title":"An adaptive regularization method in Banach spaces","authors":"S. Gratton, S. Jerad, P. Toint","doi":"10.1080/10556788.2023.2210253","DOIUrl":"https://doi.org/10.1080/10556788.2023.2210253","url":null,"abstract":"This paper considers optimization of nonconvex functionals in smooth infinite dimensional spaces. It is first proved that functionals in a class containing multivariate polynomials augmented with a sufficiently smooth regularization can be minimized by a simple linesearch-based algorithm. Sufficient smoothness depends on gradients satisfying a novel two-terms generalized Lipschitz condition. A first-order adaptive regularization method applicable to functionals with β-Hölder continuous derivatives is then proposed, that uses the linesearch approach to compute a suitable trial step. It is shown to find an ϵ-approximate first-order point in at most evaluations of the functional and its first p derivatives.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"111 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124692264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-22DOI: 10.1080/10556788.2023.2196725
A. Krylatov
Nowadays, the issue of traffic flow assignment has become an interdisciplinary topic that concerns multiple research areas and branches of science. This work is focussed on the mathematical and computational aspects of the equilibrium traffic assignment problem in the case when route flows are considered to be decision variables. Firstly, we obtain a fixed-point mapping with the explicit contraction operator, which is proven to equilibrate the journey times on feasible routes between a single origin-destination pair of nodes with the quadratic rate. Remarkable that from mathematical perspectives, the developed operator generalizes most path-equilibration operators already exploited by researchers. Secondly, we use the obtained fixed-point procedure to run the sequential path-equilibration algorithm for traffic flow assignment on well-known test urban road networks with arc-additive travel time functions. Our computational results appear to demonstrate higher accuracy of user-equilibrium traffic assignment solutions than the best ones known to us. In other words, developed within this paper sequential path-equilibration algorithm leads to solutions with less goal function values compared to the best solutions for today, according to our knowledge.
{"title":"Sequential path-equilibration algorithm for highly accurate traffic flow assignment in an urban road network","authors":"A. Krylatov","doi":"10.1080/10556788.2023.2196725","DOIUrl":"https://doi.org/10.1080/10556788.2023.2196725","url":null,"abstract":"Nowadays, the issue of traffic flow assignment has become an interdisciplinary topic that concerns multiple research areas and branches of science. This work is focussed on the mathematical and computational aspects of the equilibrium traffic assignment problem in the case when route flows are considered to be decision variables. Firstly, we obtain a fixed-point mapping with the explicit contraction operator, which is proven to equilibrate the journey times on feasible routes between a single origin-destination pair of nodes with the quadratic rate. Remarkable that from mathematical perspectives, the developed operator generalizes most path-equilibration operators already exploited by researchers. Secondly, we use the obtained fixed-point procedure to run the sequential path-equilibration algorithm for traffic flow assignment on well-known test urban road networks with arc-additive travel time functions. Our computational results appear to demonstrate higher accuracy of user-equilibrium traffic assignment solutions than the best ones known to us. In other words, developed within this paper sequential path-equilibration algorithm leads to solutions with less goal function values compared to the best solutions for today, according to our knowledge.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117002236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-19DOI: 10.1080/10556788.2023.2198769
A. Beck, R. Sharon
Fisher linear discriminant analysis (FLDA or LDA) is a well-known technique for dimension reduction and classification. The method was first formulated in 1936 by Fisher in the one-dimensional setting. In this paper, we will examine the LDA problem using a different objective function. Instead of maximizing the sum of all distances between all classes, we will define an objective function that will maximize the minimum separation among all distances between all classes. This leads to a difficult nonconvex optimization problem. We present a branch and bound method for the problem in the case where the reduction is to the one-dimensional space.
{"title":"A branch and bound method solving the max–min linear discriminant analysis problem","authors":"A. Beck, R. Sharon","doi":"10.1080/10556788.2023.2198769","DOIUrl":"https://doi.org/10.1080/10556788.2023.2198769","url":null,"abstract":"Fisher linear discriminant analysis (FLDA or LDA) is a well-known technique for dimension reduction and classification. The method was first formulated in 1936 by Fisher in the one-dimensional setting. In this paper, we will examine the LDA problem using a different objective function. Instead of maximizing the sum of all distances between all classes, we will define an objective function that will maximize the minimum separation among all distances between all classes. This leads to a difficult nonconvex optimization problem. We present a branch and bound method for the problem in the case where the reduction is to the one-dimensional space.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127084478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-19DOI: 10.1080/10556788.2023.2205644
M. Passacantando, F. Raciti
We propose a new algorithm for solving a class of linear-quadratic network games with strategic complements and bounded strategies. The algorithm is based on the sequential solution of linear systems of equations and we prove that it finds the exact Nash equilibrium of the game after a finite number of iterations. The new algorithm is then applied to a social network model of juvenile delinquency which has been investigated recently where we also consider random perturbations of some data. Experimental results show the efficiency of the algorithm in solving large scale problems.
{"title":"A finite convergence algorithm for solving linear-quadratic network games with strategic complements and bounded strategies","authors":"M. Passacantando, F. Raciti","doi":"10.1080/10556788.2023.2205644","DOIUrl":"https://doi.org/10.1080/10556788.2023.2205644","url":null,"abstract":"We propose a new algorithm for solving a class of linear-quadratic network games with strategic complements and bounded strategies. The algorithm is based on the sequential solution of linear systems of equations and we prove that it finds the exact Nash equilibrium of the game after a finite number of iterations. The new algorithm is then applied to a social network model of juvenile delinquency which has been investigated recently where we also consider random perturbations of some data. Experimental results show the efficiency of the algorithm in solving large scale problems.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124751146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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