Reformulation Of Problem Research Articles

Unconstrained optimization reformulation for stochastic nonlinear complementarity problems

We present an unconstrained optimization reformulation for the stochastic nonlinear complementarity problem in this paper, which aims at minimizing an expected residual defined by the D-gap function. We discuss the existence of a solution to the unconstrained expected residual minimization (UERM) problem. By the quasi-Monte Carlo method, we obtain the discrete approximations of the UERM problem and prove that every accumulation point of minimizers or stationary points of discrete approximation problem is La minimum or stationary point of the UERM problem. We finally apply the UERM formulation to the traffic equilibrium problem.

Conversation Analysis and Psychotherapy: Identifying Transformative Sequences

ABSTRACTThe starting point of conversation analytical research on psychotherapy was in Kathy Davis’s work on problem reformulations in the mid 1980s. Since then there has been a growing body of analysis of psychotherapy, based on the close, sequential relations between adjacent utterances. Through examples drawn from CA studies on psychotherapy in the past decade, this review shows that sequential relations between utterances enable a process of transformation of experience. This process pertains to referents, emotion, and momentary relations between the therapist and the client. The utterance-by-utterance transformation contributes to the process of change in more macroscopic time, spanning the continuum of psychotherapeutic sessions. The recent developments of CA research on psychiatric consultants will also be discussed. Data are in Finnish and English.

A Maximum Entropy Procedure to Solve Likelihood Equations.

In this article, we provide initial findings regarding the problem of solving likelihood equations by means of a maximum entropy (ME) approach. Unlike standard procedures that require equating the score function of the maximum likelihood problem at zero, we propose an alternative strategy where the score is instead used as an external informative constraint to the maximization of the convex Shannon’s entropy function. The problem involves the reparameterization of the score parameters as expected values of discrete probability distributions where probabilities need to be estimated. This leads to a simpler situation where parameters are searched in smaller (hyper) simplex space. We assessed our proposal by means of empirical case studies and a simulation study, the latter involving the most critical case of logistic regression under data separation. The results suggested that the maximum entropy reformulation of the score problem solves the likelihood equation problem. Similarly, when maximum likelihood estimation is difficult, as is the case of logistic regression under separation, the maximum entropy proposal achieved results (numerically) comparable to those obtained by the Firth’s bias-corrected approach. Overall, these first findings reveal that a maximum entropy solution can be considered as an alternative technique to solve the likelihood equation.

Real-Time Load Scheduling and Storage Management for Solar Powered Network Connected EVs

In this paper, we investigate a joint real-time load scheduling and energy storage management at a grid-connected solar powered electric vehicle. Without any a priori knowledge, we consider a finite time approach with arbitrary dynamics of system inputs. Our aim is to minimize an average aggregated system cost through joint optimization of electric vehicle's energy procurement price, load scheduling delays, photovoltaic sufficiency in terms of locally generated renewable energy mix, and battery degradation. Through subsequent modification and reformulation of the joint optimization problem, we utilize the concept of one-slot look-ahead queue stability to solve the problem by employing the Lyapunov optimization technique. We show that the joint optimization problem is separable into sub-problems, which are sequentially solved with asymptotic optimality and a bounded performance guarantee. Simulations are carried in different scenarios and under varying weather conditions. Results show that our proposed algorithm can achieve a daily electric vehicle's photovoltaic sufficiency up to 50.50%, a monthly bill reduction up to 72.61%, and a yearly reduced CO $_2$ emission level up to 6.06 kg, while meeting electric vehicle user's energy and delay requirements.

Design Ideator: A Conceptual Design Toolbox

Computer tools for embodiment and detailed engineering design (computer-aided design (CAD)) evolved rapidly in the past 35 years and are now pervasive throughout the industry. But todays commercial CAD is geometry-centric, not appropriate for early stages of design when detailed geometry and dimensions are not known. This paper describes a framework and a set of interconnected tools for conceptual design. In this system, a broad range of intuitive and experiential concept generation methods have been operationalized and implemented as databases, artifact repositories, knowledge bases, and interactive procedures to promote divergent thinking. The so-called “Design Ideator” includes methods for flexible and dynamic design problem formulation, re-formulation, and restructuring in the form of hierarchical and re-configurable morphological charts. This tool has been continuously enhanced through three phases of user studies and feedback. The main contributions of this work are as follows. First, this research has created a holistic framework with interlaced knowledge bases from a wide range of methods, as opposed to past research that have relied on single experiential only method. Second, we have formulated algorithms to support several intuitive methods, such as contextual shifting, analogical reasoning, provocative stimuli, and combinatorial play.

Optimal Time-Complexity Speed Planning for Robot Manipulators

In this paper, we consider the speed planning problem for a robotic manipulator. In particular, we present an algorithm for finding the time-optimal speed law along an assigned path that satisfies velocity and acceleration constraints and respects the maximum forces and torques allowed by the actuators. The addressed optimization problem is a finite-dimensional reformulation of the continuous-time speed optimization problem, obtained by discretizing the speed profile with $n$ points. The proposed algorithm has linear complexity with respect to $n$ and to the number of degrees of freedom. Such complexity is the best possible for this problem. Numerical tests show that the proposed algorithm is significantly faster than algorithms already existing in literature.

In silico strategies to couple production of bioethanol with growth in cyanobacteria.

Cyanobacteria have been considered as promising candidates for sustainable bioproduction from inexpensive raw materials, as they grow on light, carbon dioxide, and minimal inorganic nutrients. In this study, we present a genome-scale metabolic network model for Synechocystis sp. PCC 6803 and study the optimal design of the strain for ethanol production by using a mixed integer linear problem reformulation of a bilevel programming problem that identifies gene knockouts which lead to coupling between growth and product synthesis. Five mutants were found, where the in silico model predicts coupling between biomass growth and ethanol production in photoautotrophic conditions. The best mutant gives an in silico ethanol production of 1.054 mmol·gDW -1 ·h -1 .

COMO AS DECISÕES SÃO PRODUZIDAS? UMA PROPOSTA DE REFORMULAÇÃO DE UM PROBLEMA DE PESQUISA

O presente artigo tem por objetivo estimular o debate acerca da reformulação do seguinte problema de pesquisa: “como os juízes decidem?”. Apesar de existir um corpo qualificado de autores que investigam o referido problema, falta ainda a discussão dos atos que antecedem e fazem parte do processo de produção de uma decisão judicial. Neste sentido, foram utilizadas as entrevistas concedidas por ministros ao projeto História Oral do STF para demonstrar que, antes mesmo de uma decisão judicial ser produzida e, portanto, levada à sessão de julgamento, existem diversos momentos capazes de influenciar diretamente não apenas na convicção do magistrado, mas no direito que está sendo produzido. Sendo assim, a partir da leitura das entrevistas, da noção de backstage trazida por Goffman (1975) e da organização de momentos considerados fundamentais pelos magistrados, pretende-se destacar a necessidade em se abrir uma agenda de pesquisa para investigar problema diverso ao anteriormente mencionado, qual seja: “como as decisões são produzidas?”.

4-D Flight Trajectory Tracking: A Receding Horizon Approach Integrating Feedback Linearization and Scenario Optimization

This paper proposes a control strategy to steer an aircraft along a given reference 4-D trajectory. The aircraft has a nonlinear dynamics and is subject to constraints related to its maneuverability and to passengers comfort. Feedback linearization of the aircraft dynamics and convex relaxation of the constraints allow for a reformulation of the trajectory tracking problem that is suitable for a receding horizon implementation. Uncertainty is affecting the aircraft motion, mainly through wind, which is described as a Gaussian random field and approximated on-the-fly by a local autoregressive model. The adoption of a scenario-based minimization of the tracking error introduced by the stochastic wind disturbance preserves the problem convexity and allows obtaining a program that can be solved with limited computational effort. The wind model update jointly with the recomputation of the control action at each time step allow to account for the spatial variability of the random field and to obtain recursive feasibility of the receding horizon solution.

Coordinate Descent Full Configuration Interaction.

We develop an efficient algorithm, coordinate descent FCI (CDFCI), for the electronic structure ground-state calculation in the configuration interaction framework. CDFCI solves an unconstrained nonconvex optimization problem, which is a reformulation of the full configuration interaction eigenvalue problem, via an adaptive coordinate descent method with a deterministic compression strategy. CDFCI captures and updates appreciative determinants with different frequencies proportional to their importance. We show that CDFCI produces accurate variational energy for both static and dynamic correlation by benchmarking the binding curve of nitrogen dimer in the cc-pVDZ basis with 10-3 mHa accuracy. We also demonstrate the efficiency and accuracy of CDFCI for strongly correlated chromium dimer in the Ahlrichs VDZ basis and produce state-of-the-art variational energy.

The design of statements and the (re)formulation and resolution of open problems that address issues of social relevance with the use of digital technologies in the initial formation of Mathematics teachers

This paper presents the results obtained with an investigation, in which a pair of Mathematics graduates, participants of an Extension Course, carried out the design of a statement of open problems. This investigation also addressed a theme of social relevance, in which technologies were used so that these problems were (re)formulated and solved, with the use of technological resources, by students of Basic Education. In order for this objective to be achieved, the training teachers carried out the design activities of problems with the use of digital technologies, planning of the pedagogical practice, in which these problems would be proposed, and of execution of this practice, which occurred through a pedagogical workshop. After completing these activities, the graduates had the opportunity to discuss and reflect on the experiences of designer and teacher, so that they contributed to producing knowledge about the design of open problem statements that address issues of social relevance, (re)formulation and resolution using digital technologies, and how to propose such problems.

Convex optimization-based blind deconvolution for images taken with coherent illumination.

A rank-constrained reformulation of the blind deconvolution problem on images taken with coherent illumination is proposed. Since in the reformulation the rank constraint is imposed on a matrix that is affine in the decision variables, we propose a novel convex heuristic for the blind deconvolution problem. The proposed heuristic allows for easy incorporation of prior information on the decision variables and the use of the phase diversity concept. The convex optimization problem can be iteratively re-parameterized to obtain better estimates. The proposed methods are demonstrated on numerically illustrative examples.

Non-smooth DC-constrained optimization: constraint qualification and minimizing methodologies

ABSTRACTThis work concerns the study of a constraint qualification for non-smooth DC-constrained optimization problems, as well as the design and convergence analysis of minimizing algorithms to address the task of computing a stationary/critical point for problems of this class. Specialized algorithms for DC programming approximate the non-convex optimization problem by a sequence of convex subproblems, obtained by linearizing the second components of the involved DC (difference of convex) functions. We propose new approaches that define trial points as inexact solutions of such convex subproblems. This is a property of practical interest that substantially reduces the computational burden to compute a stationary/critical point of non-smooth DC-constrained optimization problems. One variant of the proposed algorithmic patterns is numerically assessed on a DC reformulation of an energy management problem considering a smart-grid controlled by a local actor (follower) and its interaction with a global actor (leader) in the power system.

A note on symmetries of diffusions within a martingale problem approach

A geometric reformulation of the martingale problem associated with a set of diffusion processes is proposed. This formulation, based on second-order geometry and Itô integration on manifolds, allows us to give a natural and effective definition of Lie symmetries for diffusion processes.

Inner entanglements: Narrowing the search in classical planning by problem reformulation

AbstractIn the field of automated planning, the central research focus is on domain‐independent planning engines that accept planning tasks (domain models and problem descriptions) in a description language, such as Planning Domain Definition Language, and return solution plans. The performance of planning engines can be improved by gathering additional knowledge about specific planning domain models/tasks (such as control rules) that can narrow the search for a solution plan. Such knowledge is often learned from training plans and solutions of simple tasks. Using techniques to reformulate the given planning task to incorporate additional knowledge, while keeping to the same input language, allows to exploit off‐the‐shelf planning engines. In this paper, we present inner entanglements that are relations between pairs of operators and predicates that represent the exclusivity of predicate achievement or requirement between the given operators. Inner entanglements can be encoded into a planner's input language by transforming the original planning task; hence, planning engines can exploit them. The contribution of this paper is to provide an in‐depth analysis and evaluation of inner entanglements, covering theoretical aspects such as complexity results, and an extensive empirical study using International Planning Competition benchmarks and state‐of‐the‐art planning engines.

Sharp upper and lower bounds for maximum likelihood solutions to random Gaussian bilateral inequality systems

This paper focuses on finding a solution maximizing the joint probability of satisfaction of a given set of (independent) Gaussian bilateral inequalities. A specially structured reformulation of this nonconvex optimization problem is proposed, in which all nonconvexities are embedded in a set of 2-variable functions composing the objective. From this, it is shown how a polynomial-time solvable convex relaxation can be derived. Extensive computational experiments are also reported, and compared to previously existing results, showing that the approach typically yields feasible solutions and upper bounds within much sharper confidence intervals.

Lattice Monte Carlo for quantum Hall states on a torus

Monte Carlo is one of the most useful methods to study the quantum Hall problems. In this paper, we introduce a fast lattice Monte Carlo method based on a mathematically exact reformulation of the torus quantum Hall problems from continuum to lattice. We first apply this new technique to study the Berry phase of transporting composite fermions along different closed paths enclosing or not enclosing the Fermi surface center in the half filled Landau level problem. The Monte Carlo result agrees with the phase structure we found on small systems and confirms it on much larger sizes. Several other quantities including the Coulomb energy in different Landau levels, structure factor, particle-hole symmetry are computed and discussed for various model states. In the end, based on certain knowledge of structure factor, we introduce a algorithm by which the lattice Monte Carlo efficiency is further boosted by several orders.

Assessment of Deterministic Shape Optimizations Within a Stochastic Framework for Supersonic Organic Rankine Cycle Nozzle Cascades

The design of converging–diverging blades for organic Rankine cycle (ORC) applications widely relies on automated shape-optimization processes. As a result, the optimization produces an adapted-nozzle cascade at the design conditions. However, only few works account for the uncertainties in those conditions and their consequences on cascade performance. The proposed solution, i.e., including uncertainties within the optimization routine, demands an overall huge computational cost to estimate the target output statistic at each iteration of the optimization algorithm. With the aim of understanding if this computational cost is avoidable, we study the impact of uncertainties in the design conditions on the robustness of deterministically optimized profiles. Several optimized blades, obtained with different objective functions, constraints, and design variables, are considered in the present numerical analysis, which features a turbulent compressible flow solver and a state-of-the-art uncertainty-quantification (UQ) method. By including measured field variations in the formulation of the UQ problem, we show that a deterministic shape optimization already improves the robustness of the profile with respect to the baseline configuration. Guidelines about objective functions and blade parametrizations for deterministic optimizations are also provided. Finally, a novel methodology to estimate the mass-flow-rate probability density function (PDF) for choked supersonic turbines is proposed, along with a robust reformulation of the constraint problem without increasing the computational cost.

Stationarity conditions and constraint qualifications for mathematical programs with switching constraints

In optimal control, switching structures demanding at most one control to be active at any time instance appear frequently. Discretizing such problems, a so-called mathematical program with switching constraints is obtained. Although these problems are related to other types of disjunctive programs like optimization problems with complementarity or vanishing constraints, their inherent structure makes a separate consideration necessary. Since standard constraint qualifications are likely to fail at the feasible points of switching-constrained optimization problems, stationarity notions which are weaker than the associated Karush–Kuhn–Tucker conditions need to be investigated in order to find applicable necessary optimality conditions. Furthermore, appropriately tailored constraint qualifications need to be formulated. In this paper, we introduce suitable notions of weak, Mordukhovich-, and strong stationarity for mathematical programs with switching constraints and present some associated constraint qualifications. Our findings are exploited to state necessary optimality conditions for (discretized) optimal control problems with switching constraints. Furthermore, we apply our results to optimization problems with either-or-constraints. First, a novel reformulation of such problems using switching constraints is presented. Second, the derived surrogate problem is exploited to obtain necessary optimality conditions for the original program.

Dynamic Mechanisms with Verification

We consider a principal who allocates an indivisible object among a finite number of agents who arrive on-line, each of whom prefers to have the object than not. Each agent has access to private information about the principal's payoff if he receives the object. The decision to allocate the object to an agent must be made upon arrival of an agent and is irreversible. There are no monetary transfers but he principal can inspect agents' reports at a cost and punish them. A novelty of this paper is a reformulation of this dynamic problem as a compact linear program. Using the formulation we characterize the form of the optimal mechanism and reduce the dynamic version of the inspection problem with identical distributions to an instance of the secretary problem with one fewer secretary and a modified value distribution. This reduction also allows us to derive a prophet inequality for the dynamic version of the inspection problem.