Stationarity Condition for Nonsmooth MPVCs with Constraint Set

2020 ◽  
pp. 314-321
Author(s):  
David Barilla ◽  
Giuseppe Caristi ◽  
Nader Kanzi
Keyword(s):  
Stationarity Condition ◽  
Constraint Set

scholarly journals Distributed Constrained Stochastic Subgradient Algorithms Based on Random Projection and Asynchronous Broadcast over Networks

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Junlong Zhu ◽  
Ping Xie ◽  
Qingtao Wu ◽  
Mingchuan Zhang ◽  
Ruijuan Zheng ◽  
...  
Keyword(s):  
Information Exchange ◽  
Optimal Solution ◽  
Random Projection ◽  
Learning Rate ◽  
Time Varying ◽  
Optimal Value ◽  
Constraint Set ◽  
Time Varying Networks ◽  
Subgradient Algorithms ◽  
Asymptotic Upper Bound

We consider a distributed constrained optimization problem over a time-varying network, where each agent only knows its own cost functions and its constraint set. However, the local constraint set may not be known in advance or consists of huge number of components in some applications. To deal with such cases, we propose a distributed stochastic subgradient algorithm over time-varying networks, where the estimate of each agent projects onto its constraint set by using random projection technique and the implement of information exchange between agents by employing asynchronous broadcast communication protocol. We show that our proposed algorithm is convergent with probability 1 by choosing suitable learning rate. For constant learning rate, we obtain an error bound, which is defined as the expected distance between the estimates of agent and the optimal solution. We also establish an asymptotic upper bound between the global objective function value at the average of the estimates and the optimal value.

scholarly journals A Quasi-Monte-Carlo-Based Feasible Sequential System of Linear Equations Method for Stochastic Programs with Recourse

2017 ◽  
Vol 2017 ◽  
pp. 1-15
Author(s):  
Changyin Zhou ◽  
Rui Su ◽  
Zhihui Jiang
Keyword(s):  
Monte Carlo ◽  
Linear Equations ◽  
Inequality Constraints ◽  
System Of Linear Equations ◽  
Active Constraint ◽  
Stochastic Programs ◽  
Quasi Monte Carlo ◽  
Sequential System ◽  
Constraint Set ◽  
A New Technique

A two-stage stochastic quadratic programming problem with inequality constraints is considered. By quasi-Monte-Carlo-based approximations of the objective function and its first derivative, a feasible sequential system of linear equations method is proposed. A new technique to update the active constraint set is suggested. We show that the sequence generated by the proposed algorithm converges globally to a Karush-Kuhn-Tucker (KKT) point of the problem. In particular, the convergence rate is locally superlinear under some additional conditions.

scholarly journals Substance matters: a reply to Jardine (2016)

Phonology ◽  
2018 ◽  
Vol 35 (1) ◽  
pp. 151-156 ◽  
Author(s):  
Joe Pater
Keyword(s):  
Optimality Theory ◽  
Constraint Set ◽  
Tonal Patterns ◽  
Formal Distinction

Jardine (2016) claims that tonal phonology is more formally complex than the phonology of other segmental features, in that only tonal phonology goes beyond the class of weakly deterministic maps. He then goes on to argue that this formal distinction is superior to any available treatment in Optimality Theory. This reply points out that Jardine's formal distinction conflates attested and unattested tonal patterns, which can be distinguished in Optimality Theory, given a substantively defined constraint set.

scholarly journals Functional Modeling of Human Perceptual Guidance using Constraint Set Analysis

2019 ◽  
Vol 51 (34) ◽  
pp. 67-74
Author(s):  
Andrew Feit ◽  
Bérénice Mettler
Keyword(s):  
Functional Modeling ◽  
Constraint Set

scholarly journals Formulation of Broiler Finishing Rations by Quadratic Programming

1986 ◽  
Vol 18 (1) ◽  
pp. 141-150 ◽  
Author(s):  
Bill R. Miller ◽  
Ronaldo A. Arraes ◽  
Gene M. Pesti
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Programming Model ◽  
Nutrition Knowledge ◽  
Information Analysis ◽  
Response Information ◽  
Constraint Set ◽  
Protein Density ◽  
Production Response ◽  
Reducing Energy

AbstractLeast cost feed mix by linear programming (LP) is a standard economic analysis in the poultry industry. A significant body of nutrition knowledge is now contained in the constraint set of industry LP models. This knowledge might be merged into an improved economic model that contains production response information. Analysis using a quadratic programming model indicated that a leading broiler firm could have improved economic efficiency by increasing protein density and reducing energy density of broiler finisher feed. If applicable industry wide, similar savings could be as high as $120 million per year.

scholarly journals Distributed Event-Triggered Subgradient Method for Convex Optimization with a Common Constraint Set

2017 ◽  
Vol 50 (1) ◽  
pp. 15319-15324 ◽  
Author(s):  
Yuichi Kajiyama ◽  
Naoki Hayashi ◽  
Shigemasa Takai
Keyword(s):  
Convex Optimization ◽  
Subgradient Method ◽  
Constraint Set ◽  
Event Triggered

scholarly journals Revisiting Projection-Free Optimization for Strongly Convex Constraint Sets

2019 ◽  
Vol 33 ◽  
pp. 1576-1583
Author(s):  
Jarrid Rector-Brooks ◽  
Jun-Kun Wang ◽  
Barzan Mozafari
Keyword(s):  
High Probability ◽  
Line Search ◽  
Convergence Rates ◽  
Global Optimum ◽  
Smooth Functions ◽  
Convex Constraint ◽  
Strongly Convex ◽  
Locally Lipschitz ◽  
Constraint Set ◽  
Constraint Sets

We revisit the Frank-Wolfe (FW) optimization under strongly convex constraint sets. We provide a faster convergence rate for FW without line search, showing that a previously overlooked variant of FW is indeed faster than the standard variant. With line search, we show that FW can converge to the global optimum, even for smooth functions that are not convex, but are quasi-convex and locally-Lipschitz. We also show that, for the general case of (smooth) non-convex functions, FW with line search converges with high probability to a stationary point at a rate of O(1/t), as long as the constraint set is strongly convex—one of the fastest convergence rates in non-convex optimization.

scholarly journals Topology optimization of trusses using bars exchange method

2012 ◽  
Vol 60 (2) ◽  
pp. 185-189 ◽  
Author(s):  
D. Bojczuk ◽  
A. Rębosz-Kurdek
Keyword(s):  
Topology Optimization ◽  
Cost Minimization ◽  
Exchange Method ◽  
Cross Sectional ◽  
First Case ◽  
Constraint Set ◽  
Topology Optimization Of Trusses ◽  
The Cost ◽  
Multiple Load Case ◽  
Multiple Load

Abstract. The algorithm of optimization of trusses is presented in the paper, where for topology optimization the bars exchange method is used. In the first case, the problem aimed at cost minimization with a constraint set on global stiffness is formulated. In the second case, the problem of minimizing the cost function subjected to stress and cross-sectional area constraints is discussed and here the multiple-load case is taken into consideration. The conditions for introduction of topology modification and its acceptance are specified. The paper is illustrated with three examples.

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