A recent series of papers has examined the extension of disjunctive-programming techniques to mixed-integer second-order-cone programming. For example, it has been shown—by several authors using ...different techniques—that the convex hull of the intersection of an ellipsoid,
E
, and a split disjunction,
(
l
-
x
j
)
(
x
j
-
u
)
≤
0
with
l
<
u
, equals the intersection of
E
with an additional second-order-cone representable (SOCr) set. In this paper, we study more general intersections of the form
K
∩
Q
and
K
∩
Q
∩
H
, where
K
is a SOCr cone,
Q
is a nonconvex cone defined by a single homogeneous quadratic, and
H
is an affine hyperplane. Under several easy-to-verify conditions, we derive simple, computable convex relaxations
K
∩
S
and
K
∩
S
∩
H
, where
S
is a SOCr cone. Under further conditions, we prove that these two sets capture precisely the corresponding conic/convex hulls. Our approach unifies and extends previous results, and we illustrate its applicability and generality with many examples.
Anyone Can Code Arya, Ali
2021, 20201123, 2020, 2020-11-24, 2020-11-23
eBook
“Ali Arya guides you in a fantastic journey full of creativity in a coherent way that allows the traveler to learn and build up over the knowledge acquired in previous chapters until the reader ...accomplishes skills to develop solutions using programming.”
—
Andrés A. Navarro Newball
, Professor, Pontificia Universidad Javeriana Cali Colombia
“An excellent book that teaches programming and software development the way it should be done: independent from a specific implementation language and focusing on the main principles that are fundamental and substantive to any kind of software production.”
—
Dr Marc Conrad
, Principal Lecturer, University of Bedfordshire
Anyone Can Code: The Art and Science of Logical Creativity
introduces computer programming as a way of problem-solving through logical thinking. It uses the notion of Modularization as a central lens through which we can make sense of many software concepts. The book takes the reader through fundamental concepts in programming by illustrating them in three different and distinct languages, C/C++, Python, and Javascript.
Key features:
Focuses on problem-solving and algorithmic thinking instead of programming functions, syntax, and libraries.
Includes engaging examples, including video games and visual effects
Provides exercises and reflective questions.
It gives the beginner and intermediate learners a strong understanding of what they are doing so that they can do it better and with any other tool or language that they may end up using later.
About the Author:
Ali Arya is an Associate Professor of Information Technology at Carleton University, Ottawa, Canada. He received his Ph.D. in Computer Engineering from the University of British Columbia in 2003. Ali has over 25 years of experience in professional and academic positions related to software development and information technology. He is passionate about computer programming that brings together logical and creative abilities.
Unit commitment (UC) is a key operational problem in power systems for the optimal schedule of daily generation commitment. Incorporating uncertainty in this already difficult mixed-integer ...optimization problem introduces significant computational challenges. Most existing stochastic UC models consider either a two-stage decision structure, where the commitment schedule for the entire planning horizon is decided before the uncertainty is realized, or a multistage stochastic programming model with relatively small scenario trees to ensure tractability. We propose a new type of decomposition algorithm, based on the recently proposed framework of stochastic dual dynamic integer programming (SDDiP), to solve the multistage stochastic unit commitment (MSUC) problem. We propose a variety of computational enhancements to SDDiP, and conduct systematic and extensive computational experiments to demonstrate that the proposed method is able to handle elaborate stochastic processes and can solve MSUCs with a huge number of scenarios that are impossible to handle by existing methods.
This open access book constitutes the proceedings of the 32nd European Symposium on Programming, ESOP 2023, which was held during April 22-27, 2023, in Paris, France, as part of the European Joint ...Conferences on Theory and Practice of Software, ETAPS 2023. The 20 regular papers presented in this volume were carefully reviewed and selected from 55 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems.
Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such ...problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution.
Several prescriptive tasks in business and engineering as well as prediction in machine learning entail the solution of challenging discrete optimization problems. We recast the typical optimization ...formulation of these problems as high-dimensional dynamic programs and approach their approximation via linear programming. We develop tractable approximate linear programs with supporting theory by bringing together tools from state-space aggregations, networks, and perfect graphs (i.e., graph completions). We embed these models in a simple branch-and-bound scheme to solve applications in marketing analytics and the maintenance of energy or city-owned assets. We find that the resulting technique substantially outperforms a state-of-the-art commercial solver as well as aggregation-heuristics in terms of both solution quality and time. Our results motivate further consideration of networks and graph theory in approximate linear programming for solving deterministic and stochastic discrete optimization problems.
We present relaxations for discrete optimization problems using approximate linear programs (ALPs) defined on multiple networks that represent different state-space aggregations. Our network ALP leverages information across these networks using a piecewise-constant value function approximation, and its optimistic bound is theoretically guaranteed to weakly improve upon the bounds from the individual networks used in its construction. Solving network ALPs is challenging because of its large number of constraints—a well-known issue when employing approximate linear programming. We side-step this issue by using a clique-based graph representation to design a network ALP restriction that admits a polynomial-time solvable extended formulation, which we show to also deliver a weakly better bound than individual networks. We execute a computational study on a challenging bilinear problem arising in marketing analytics and a routing application encountered in the preemptive maintenance of energy or city-owned assets. When used within a branch-and-bound scheme, the network ALP restriction significantly outperforms in both solution quality and time the following benchmarks: a state-of-the-art mathematical programming solver, a generic aggregation/disaggregation scheme applied to a single network, and a heuristic that chooses the best bound among individual networks.
A parallel automated resilience-based restoration methodology is presented in the power system to minimize impact due to emergency power outages. In this power restoration process, a black start unit ...is assigned to a small region (i.e., a section) on an as-needed basis. A mixed integer nonlinear programming model is developed in order to optimally sectionalize the region of interest all the while maximizing the resiliency in terms of load shedding, restoration time, and network connectivity. For solving this large scale optimization model, a bi-level programming approach is proposed. This approach consists of two optimization levels. The sectionalization problem (upper level) is a mixed integer programming model and finds the optimal section set. The restoration problem (lower level) is a linear model and determines the dc optimal power flow and restoration time for the optimal section set identified in the upper level. We use the pre-emptive method of goal programming to deal with multiple conflicting objectives in the model. Our proposed solution approach outperformed mathematical programming with equilibrium constraints and found near optimal solutions. Numerical results and sensitivity analysis from two case studies (6- and 118-bus IEEE test systems) are further discussed to demonstrate the efficiency of the solution approach.
Learn the theory behind cross-platform development, and put the theory into practice with code using the invaluable information presented in this book. With in-depth coverage of development and ...distribution techniques for iPhone, BlackBerry, Windows Mobile, and Android, you'll learn the native approach to working with each of these platforms. With detailed coverage of emerging frameworks like PhoneGap and Rhomobile, you'll learn the art of creating applications that will run across all devices. You'll also be introduced to the code-signing process and the distribution of applications through the major application stores, including RIM, Apple, and Microsoft.
A multitude of different probabilistic programming languages exists today, all extending a traditional programming language with primitives to support modeling of complex, structured probability ...distributions. Each of these languages employs its own probabilistic primitives, and comes with a particular syntax, semantics and inference procedure. This makes it hard to understand the underlying programming concepts and appreciate the differences between the different languages. To obtain a better understanding of probabilistic programming, we identify a number of core programming concepts underlying the primitives used by various probabilistic languages, discuss the execution mechanisms that they require and use these to position and survey state-of-the-art probabilistic languages and their implementation. While doing so, we focus on probabilistic extensions of
logic
programming languages such as Prolog, which have been considered for over 20 years.
Successful transition to active distribution networks (ADNs) requires a planning methodology that includes an accurate network model and accounts for the major sources of uncertainty. Considering ...these two essential features, this paper proposes a novel model for the multistage distribution expansion planning (MDEP) problem, which is able to jointly expand both the network assets (feeders and substations) and renewable/conventional distributed generators. With respect to network characteristics, the proposed planning model employs a convex conic quadratic format of ac power flow equations that is linearized using a highly accurate polyhedral-based linearization method. Furthermore, a chance-constrained programming approach is utilized to deal with the uncertain renewables and loads. In this regard, as the probability distribution functions of uncertain parameters are not perfectly known, a distributionally robust (DR) reformulation is proposed for the chance constraints that guarantees the robustness of the expansion plans against all uncertainty distributions defined within a moment-based ambiguity set. Effective linearization techniques are also devised to eliminate the nonlinearities of the proposed DR reformulation, which yields a distributionally robust chance-constrained mixed-integer linear programming model for the MDEP problem of ADNs. Finally, the 24-node and 138-node test systems are used to demonstrate the effectiveness of the proposed planning methodology.
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