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1
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1answer
24 views

Convex Optimization problem with sum of absolute value constraints

How to solve the optimization problem written below? $$\begin{align} &\operatorname{argmax}\limits_{a}\; a^T b - \frac{1}{2} a^T X a\\ &\text{subject to } \sum_i |a_i|=4,\; \sum_i a_i = 0 ...
2
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0answers
24 views

Disjunctive programming software

Can you advise me any kind of existing software that can help to solve the disjunctive programming problem? The problem is the following. We have unit 3D planes $\Pi_{1}, \ldots, \Pi_{N}$ (they are ...
0
votes
0answers
21 views

can I cast $\mathrm{vec}(X^TX)$ with matrix $X$ into quadratic form of $\mathrm{vec}(X)$

I want to cast $\min \mathrm{tr}\,J(X^TX-C)$ where $J=$ all one's matrix (this is just sum of all elements in $X^TX-C$) with matrix $X$ into standard quadratic program. The natural way is to use ...
2
votes
1answer
106 views

Solve $AX = B$ where $X^T X = C$

Is there a natural way to find the solution to $$AX = B, X^TX = C \enspace \text{?}$$ $X$ is a matrix and has a small number of rows, and $A$ is sparse. An approximate solution would be fine.
1
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2answers
59 views

Solving absolute value quadratic optimization problem

would you please help me to solve following problem $$x^*= \text{argmin}\ xLx^T+ |P^Tx|$$ $x$ is binary $P$ is a known vector (with positive and negative values) $L$ is Laplacian matrix I have ...
0
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2answers
84 views

Convex quadratic problem solver gives different answers?

I'm not a mathematics girl but I'm pretty sure that the following variance objective function should be a convex quadratic problem. My objective function is as follows: $$ \text{argmin } \text{var ...
1
vote
0answers
18 views

Vector of Lagrangian of QP at solution

I am trying to understand the output of the quadprog R package for quadratic programming. The problem I have is the vector with the Lagragian at the solution (object "Lagrangian" of the output). My ...
0
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0answers
9 views

estimate of direction of lowest stiffness on function from random samples

Assume I have scalar function defined on $n$-dimensional space $y: R^n \rightarrow R $ sampled at $m$ points $\vec x_i$ with values $y_i = y({\vec x_i})$. Assume that the function $y(\vec x)$ can be ...
2
votes
1answer
118 views

Solving the quadratic in the Fast Iterative Method

The Fast Iterative Method is a way of solving the Eikonal Equation on a discrete grid, similar to the Fast Marching Method discussed in another question here. The paper describes the overall ...
1
vote
1answer
97 views

Mixed-integer quadratic programming, state of art [closed]

I used Gurobi with a MIQP with 26 binary variables and 26*4 interaction term without any other constraint. The speed is very slow already.... I want to ask what is the state of art of MIQP solvers. ...
1
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3answers
172 views

Minimize quadratic form with equality constraints

I want to minimize function: $f(x) = x^T \cdot A \cdot x + b \cdot x$ given constraints: $B \cdot x = 0$. Here: $x$ is a vector ($x \in \mathbb{R}^n$), $A$ is a matrix of size $n \times n$, $b$ ...
1
vote
3answers
109 views

rank-deficient NNLS

I want to find the minimum-norm solution to a rank-deficient least-squares problem, subject to positivity constraints, e.g. $$\min_x\ \|x\|^2 \quad s.t.\quad Ax = b,\ x \geq 0$$ where $A$ is large, ...
2
votes
1answer
173 views

0,1 binary polynomial programming

Is there a mathematical optimization branch that explicitly tries to optimize this (type) problem? $$\eqalign{ & \min \cr & \sum\limits_{i = 1}^N {(J*s[i] + {J_1}*s[i]*s[i + 1] + ...
1
vote
1answer
127 views

How can a quadratic positive definite minimization be unbounded [closed]

I am minimising a diagonal quadratic matrix using CPLEX. All off diagonal elements are zero. It has 500 variables and 20 linear constraints plus each variable is constrained to be within 0 and 1 All ...
3
votes
2answers
95 views

A separable nonnegative quadratic program

I have spent quite some time trying to solve the following quadratic program: $$\min \sum_{i=1}^n (\frac{1}{2}x_i^TQx_i+c_i^Tx_i), \quad \mathrm{s.t. } \quad x_i\ge 0 \quad \forall i,$$ where $n$ is ...
0
votes
1answer
356 views

CPLEX claims to have solved QP minimisation but solution is not optimal

I am trying to solve a small QP problem in CPLEX. The problem has several linear constraints. The optimiser runs and finds a solution which satisfies these constraints and CPLEX returns a success ...
3
votes
1answer
152 views

Sparse quadratic programming solver

For a hobby project I need to solve a series of quadratic programming problems each with about 500 variables about 1000 constraints, each of the form $x_i-x_j\le c_{ij}$ the objective function is ...
4
votes
3answers
106 views

Plane constraints in R3

I have multiple plane constraints in $\mathbb{R}^3$ of the form: $$n_i \cdot x \ge \delta_i$$ Where $n_i$ is the $i$th plane normal (in form (x, y, z)), $x$ is a point in space, and $\delta_i$ is ...
0
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0answers
104 views

Numerical integral with a weakly singular kernel with a satisfactory precision

I am working on numerical method for time fractional PDE. One problem is that I must compute numerical integral with the following form: \begin{equation} \int_0^{t_m} (t_m-s)^{-\beta}f(s)ds ...
1
vote
1answer
189 views

Quadratic Programming bound constraints

I have a quadratic programming problem with constraints of the general form: Minimize w.r.t. x: f(x) = (1/2) x^T * Q * x + c^T * x subject to one or more ...
4
votes
1answer
261 views

Solver suggestion for many small quadratic problem in C++

I have a C++ program/model that in some parts already use IPOPT (with ADOL-C and ColPack) to solve some pretty large non linear problems. Now in an other part of the program I need to solve a large ...
0
votes
0answers
96 views

Quadratic programming problem involving permutation matrices

Does anyone know a good algorithm for quickly finding an approximate solution to the following problem? Given two square matrices $A$ and $B$, minimize $\| P A P^\top - B \|$ over all permutation ...
0
votes
1answer
141 views

Modeling a quadratic constraint with a linear expression

In a problem I am trying to model with a MIP program, the following scenario occurs: I am given binary variables $x_1,\ldots,x_n$ and $y_1,\ldots,y_n$ which can really be regarded as $n$-vectors. ...
1
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0answers
82 views

Quadratic optimization without any cross terms

I need to solve a quadratic program in Java which minimizes a sum of squares. The problem is that there are constraints to be satisfied, and so a quadratic optimizer must be used. I've been thinking ...
3
votes
2answers
277 views

Quadratic Programming: Quadprog

Given a real-rectangular matrix $S$ and inorder to solve this simple quadratic programming problem: Minimize $w'S'Sw = ||S w||^2$ over $w$ subject to $e^Tw = 1$ and $w \geq 0$ using a solver I ...
1
vote
0answers
99 views

Cplex C++ Interface: Repeated calls of setQuadCoef are slow. Is there an alternative?

I noticed that repeated calls of the member function setQuadCoef of the class IloObjective can be prohibitively slow. The Cplex ...
3
votes
2answers
217 views

Solver for a MIQP with an indefinite coefficient matrix

Do CPLEX or Gurobi handle MIQPs with indefinite coefficient matrices? The problem I am dealing with has quadratic terms in which one variable is binary and the other variable is continuous. The ...
4
votes
1answer
1k views

Why does MATLAB's quadprog outperform MOSEK for my problem?

For a problem I am trying to solve it appears MOSEK's Quadratic Program solver is 100 times slower than MATLAB's Interior Point solver. Has anyone encountered this behavior in the past, or maybe ...
2
votes
2answers
523 views

Quadratic program With Linear Constraint vs. Eigen Decomposition Time Complexity-Comparison. Which is faster?

Say I had the choice of choosing one out of the following two optimization problems which I could use to solve my problem. Which choice is the fastest? How much of a trade-off would it be-as in - Is ...
5
votes
2answers
143 views

What is a suitable algorithm for solving a large mixed-integer quadratic program?

I am interested in the solutions of a very large quadratic programming (QP) problem \begin{align} \min_{x \in \mathbb{R}^n} & x^T Q x\\ \mathrm{subject\ to} & A x = b\\ & x \in \{0,1\}^n ...
9
votes
2answers
800 views

Calculating Lagrange coefficients for SVM in Python

I'm trying to write a full SVM implementation in Python and I have a few issues computing the Lagrange coefficients. First let me rephrase what I understand from the algorithm to make sure I'm on the ...