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1
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3answers
83 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
81 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
162 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
77 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
84 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
141 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 ...
2
votes
1answer
78 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
98 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
votes
0answers
35 views

Linear complementarity problems with inequality (box) constraints

I can find many references and matlab or c++ codes for solving each problem separately. But it is very hard to find one that actually solve both simultaneously on the internet. I am quite sure that ...
0
votes
0answers
57 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
122 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
134 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
79 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
74 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
vote
0answers
78 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
231 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
82 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
136 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
910 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
446 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
133 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
605 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 ...