Optimization and Applications: 10th International Conference, OPTIMA 2019, Petrovac, Montenegro, September 30 – October 4, 2019, Revised Selected ... in Computer and Information Science, 1145) 9783030386023, 9783030386030, 3030386023

Table of contents :
Preface
Organization
Invited Talks
Quasistatic Evolution Variational Inequalities and Sweeping Process
Relative Smoothness: New Paradigm in Convex Optimization
Necessary Conditions for an Extended Weak Minimum in Optimal Control Problems with Volterra-Type Integral Equations on a Variable Time Interval
High-Performance Optimization
Contents
Efficient Algorithms for the Routing Open Shop with Unrelated Travel Times on Cacti
1 Introduction
2 Problem Formulation and Preliminary Notes
2.1 Formulation and Notation
2.2 Instance Simplification Operations
2.3 Superoverloaded Nodes and Unrelated Travel Times
3 Extended Instance Reduction
4 Optima Localization for the Cycleless Instances on a Cactus
5 Conclusion
References
Local Strong Convexity in Hilbert Space
1 Introduction and Main Notations
2 Lipschitz Property for Metric Projection on the Subset of Boundary
3 Local Strong Convexity of the Subset of Boundary with Lipschitz Property with Constant Less Than 1
4 Further Plans
References
Semidefinite Relaxation and Sign-Definiteness of Quadratic Forms on the Cone
1 Introduction
2 Semidefinite Relaxation and the S–Procedure
3 Criteria of Conditional Sign Definiteness and Absence of Conditional Sign Definiteness
4 Conclusion
References
Distance-Constrained Line Routing Problem
1 Introduction
2 Statement of the Problem and Preliminary Analysis
3 The Existence of Solution
4 Algorithms
5 Conclusion
References
Problems of Synthesis, Analysis and Optimization of Parameters for Multidimensional Mathematical Models of Interconnected Populations Dynamics
1 Introduction
2 Constructing of Deterministic Models
3 Analysis of Model Examples in the Deterministic Case
4 Stochastic Models
5 The Problem of Optimal Control in Models of the Populations Dynamics
6 Conclusions
References
Lipschitz Continuity of the Optimal Solution of the Infimal Convolution Problem and Subdifferential Calculus
1 Introduction
2 Weakly Convex Sets and Functions: Motivating Examples and Definitions
3 Well-Posedness of the Problem and Continuity of the Optimal Solution
4 Lipschitz Continuity of the Optimal Solution
5 Subdifferential Calculus and Lower Regularity of the Optimal Value Function
6 Conclusion
References
Polynomial-Time Solvability of One Optimization Problem Induced by Processing and Analyzing Quasiperiodic ECG and PPG Signals
1 Introduction
2 Data Generation and Approximation Models
3 Optimization Problem
4 Algorithm
5 Examples of Numerical Experiments
6 Conclusion
References
Equity-Linked Notes Portfolio Optimization
1 Introduction
2 Pricing Model
3 ELN Portfolio Optimization Problem
4 Transformation the Optimization Problem to the Dynamic Programming Equation
5 Conclusion
References
On Optimization Problem Arising in Computer Simulation of Crystal Structures
1 Introduction
2 Algorithm for Computing Hessian of the Cost Function
3 Calculation the Hessian of the Energy for a Two-Dimensional Material Model with the Unloaded Condition
4 Conclusion
References
On the Complexity of Some Quadratic Euclidean Partition Problems into Balanced Clusters
1 Introduction
2 Problem Statement and Related Problems
3 Complexity Analysis
4 Conclusion
References
An Approximate Solution of a GNSS Satellite Selection Problem Using Semidefinite Programming
1 Introduction
2 Proposed Method
2.1 Linear Relaxation
2.2 SDP Problem
2.3 SOCP Problem
2.4 Selection Algorithm
2.5 Upper Bound of GDOP Error
3 Experimental Study
3.1 Results for One Epoch
3.2 Accuracy Evaluation
3.3 Calculation Time Evaluation
4 Conclusion
References
Dynamic Marketing Model: The Case of Piece-Wise Constant Pricing
1 Introduction
2 Two Marketing Models
2.1 Pricing
2.2 Profits and Motion
2.3 Maximization of Manufacturer's Profit Under Constant Pass-Through
2.4 Maximization of Retailer's Profit Under Constant Wholesale Discount
3 Maximization of Manufacturer's and Retailer's Profits
3.1 The Case: Wholesale Discount and Pass-Through Are Constant
4 The Case: Wholesale Discount and Pass-Through Are Piece-Wise Constant
4.1 Main Result: The Strict Concavity of Retailer's Profit
5 Proofs
5.1 Proof of Proposition 1
5.2 Proof of Proposition 2
6 Conclusion
References
Preconditioned Subspace Descent Methods for the Solution of Nonlinear Systems of Equations
1 Introduction
2 Preconditioned Subspace Descent
2.1 General Estimate for Residual Norm Reduction
2.2 Practical Method for Choosing the Stepsize
2.3 Bounding the Limiting Stepsize *
2.4 Reducing the Angle Between f and Jp
2.5 Regularizing Subspace Projection with Account for *
2.6 The Use of Preconditioning
2.7 Description of Computational Algorithm
3 Test Problems and Numerical Results
3.1 Rosenbrock Function
3.2 Biggs6 Test Function
3.3 Broyden Tridiagonal Function
3.4 Chained Rosenbrock Function
3.5 Approximate Canonical Decomposition of Dense 3D Tensor
3.6 Canonical Decomposition of Matrix Multiplication Tensor
3.7 Flow in a Porous Medium 2D Problem
4 Concluding Remarks
References
Comparison of Direct and Indirect Approaches for Numerical Solution of the Optimal Control Problem by Evolutionary Methods
1 Introduction
2 The Problem of Optimal Control
3 The Problem of Synthesized Optimal Control
4 A Comparative Example
4.1 The Direct Approach
4.2 Synthesized Optimal Control
5 Conclusion
References
On PTAS for the Geometric Maximum Connected k-Factor Problem
1 Introduction
1.1 Related Work
1.2 Preliminaries
2 Approximation Algorithms
2.1 Algorithm APSP for the Geometric Maximum m-PSP
2.2 Asymptotically Optimal Algorithm A"0365A for the Geometric Maximum k-CFP in Case of Small k
2.3 PTAS and Asymptotically Optimal Algorithm in Case of Arbitrary k
3 Conclusion
References
Generalization of Controls Bimodality Property in the Optimal Exploitation Problem for Ecological Population with Binary Structure
1 Introduction
2 Some Definitions, Notation and Preliminary Results
3 Properties of Quasi-preserving Controls for the Generalization of the Leslie Model
4 Conclusion
References
On a Global Search in D.C. Optimization Problems
1 Introduction
2 Problem Statement
3 The Exact Penalty
4 Global Optimality Conditions (GOC)
4.1 A Theoretical Method
4.2 A Global Search Scheme
4.3 Convergence of the GSS1
5 Conclusion
References
P-Regularity Theory and Nonlinear Optimization Problems
1 Non-linear Optimization Problem Formulation
2 Generalization of p-factor Lyusternik Theorem and p-order Implicit Function Theorem
3 Some Generalization of Lyusternik Theorem on Tangent Cone
References
Optimization of Kernel Estimators of Probability Densities
1 The Constructive Kernel Algorithm for Approximation of Probability Densities
2 Optimization Using the Upper Boundary of Error: Choice of the Kernel Function and the Blur Coefficient
3 The Randomized Projection-Mesh Functional Algorithm for Solving of the Fredholm Integral Equation of the Second Kind
4 Conditional Optimization of the Kernel Algorithm
5 Conclusion
References
Golden Rule Saving Rate for an Endogenous Production Function
1 Introduction
2 Solow Model in Terms of Capacity and Labor Intensity
3 An Exogenous Production Function
4 Golden Rule for the Endogenous Production Function
5 Conclusions and Implication
References
Computational Methods for the Stable Dynamic Model
1 Introduction
1.1 Contents
1.2 Notation
2 Stable Dynamic Model and Its Representations
2.1 Stable Dynamic Model
2.2 Linear Programming Representation of the Stable Dynamic Model
2.3 Node Potentials Representation
2.4 Saddle-Point Representation
3 Smoothed Version of the Stable Dynamic Model
3.1 Optimality Conditions for SVSD-Model
4 Computational Techniques for the Stochastic Equilibrium Problems
5 Numerical Experiments
6 Conclusion
References
Dual Multiplicative-Barrier Methods for Linear Second-Order Cone Programming
1 Introduction
2 Primal and Dual SOCP Problems
3 The Iterative Processes
4 The Other Form of the Feasible Method
5 The Local Convergence
References
A Problem of Scheduling Operations at a Locomotive Maintenance Depot
1 Introduction
2 Problem Statement
3 Constraint Programming Model
3.1 Decision Variables, Functions and Other Denotations
3.2 Objective Functions
3.3 Constraints
4 Greedy Algorithm
5 Results and Conclusions
References
An Experimental Study of Univariate Global Optimization Algorithms for Finding the Shape Parameter in Radial Basis Functions
1 Introduction
2 Problem Statement
2.1 Statement of the Interpolation Problem
2.2 Statement of the Optimization Problem
3 Algorithms and Organization of Experiments
4 Results of Numerical Experiments
5 Conclusion
References
Time-Optimal Control Problem with State Constraints in a Time-Periodic Flow Field
1 Introduction
2 Problem Formulation: Navigation Problem
2.1 Regularity Condition
3 Maximum Principle
4 Applications: Control Set Constrained to the Square
4.1 Sufficient Condition for Regularity
4.2 Explicit Formulas for u* and
5 Numerical Results
6 Conclusion
References
The Generalized Ellipsoid Method and Its Implementation
1 Introduction
2 The Generalized Ellipsoid Method and Its Properties
2.1 The B-Form of the Generalized Ellipsoid Method
2.2 The H-Form of the Generalized Ellipsoid Method
2.3 Special Cases of the Generalized Ellipsoid Method
3 Algorithm Emshor for Minimizing Convex Functions
3.1 Algorithm Emshor
3.2 Octave Function Emshor
3.3 Computational Experiments for Ravine Function
4 Other Applications of the Generalized Ellipsoid Method
4.1 Constrained Convex Programming
4.2 Saddle Point Problems of Convex-Concave Functions
4.3 Possible Ways of Accelerating the Ellipsoid Method
5 Conclusion
References
Investigation of the Problem of Optimal Control by a System ODE of Block Structure with Blocks Connected only by Boundary Conditions
1 Introduction
2 Problem Statement
3 Necessary Optimality Conditions in Problem (1)–(4)
4 Conclusion
References
A Graph-Theoretic Approach to Multiobjective Permutation-Based Optimization
1 Introduction
2 Embedding into Euclidean Space and Graph-Theoretic Approaches to Solving COP
3 Permutation-Based Optimization Problems
4 Generalized Coordinate Method (GCM) for PB-LOP1
5 GLCM Illustration
6 GLM for Permutation-Based Multiobjective Linear Optimization
7 Conclusion
References
A Smoothing Lagrange Multiplier Method for Solving the Quasi-variational Signorini's Inequality
1 Introduction
2 Semicoercive Contact Problem in Elasticity with Friction. Quasi-Variational Inequality
3 Sensitivity Functional and Modified Lagrangian Functional
4 Uzawa Gradient Method
5 Conclusion
References
Polynomial Capacity Guarantees PTAS for the Euclidean Capacitated Vehicle Routing Problem Even for Non-uniform Non-splittable Demand
1 Introduction
2 Related Work
3 Problem Statement
4 Main Idea
5 Dynamic Programming
5.1 Proof Sketch
6 Conclusion
References
New Version of Mirror Prox for Variational Inequalities with Adaptation to Inexactness
1 Introduction
2 Problem Statement and Some Examples
3 Adaptive Method for Variational Inequalities with Adaptation to Inexactness
4 Numerical Experiments for Non-Smooth Optimization Problem: Variational Inequality for Some Analogue of Fermat-Torricelli-Steiner Problem
5 Numerical Experiments for Matrix Games with Inexactness
6 Conclusion
References
Computational Experience and Challenges with the Conjugate Epi-Projection Algorithms for Non-smooth Optimization
1 Notations and Preliminaries
2 Conjugate Epi-Projection Algorithm
2.1 Basic Computational Scheme
2.2 Implementation Issues
2.3 Numerical Example
3 Conjugate Epi-Projection Algorithm with a Skew Cut
3.1 Projection in Modified Support-Update Step
References
A Criterion of Optimality of Some Parallelization Scheme for Backtrack Search Problem in Binary Trees
1 Introduction
2 Problem Statement
3 Related Work
4 Main Result
5 Conclusions
References
Well Posedness of the Nearest Points Problem for Two Sets in Asymmetric Seminormed Spaces
1 Introduction
2 Definitions and Notation
3 Motivation of the Problem
4 Auxiliary Results
5 Main Result
6 Conclusion
References
Two Optimization Problems for a Material Point Moving Along a Straight Line in the Presence of Friction and Limitation on the Velocity
1 Introduction
2 Time Optimal Control Problem
3 The Dubovitskii-Milyutin Maximum Principle for Time Optimal Control Problem
3.1 Maximum Principle for a General Problem of the Type A
3.2 Maximum Principle for Problem A
4 Extremals of Problem A
5 Energy Optimal Control Problem
6 The Dubovitskii-Milyutin Maximum Principle for Energy Optimal Control Problem
6.1 Maximum Principle for a General Problem of the Type B
6.2 Maximum Principle for Problem B
7 Extremals of Problem B
8 Conclusions
References
Author Index